diff --git a/data/gps1.g b/data/gps1.g index 638cf30..7539fc1 100644 --- a/data/gps1.g +++ b/data/gps1.g @@ -54,8 +54,8 @@ PGAlt, PGSym, ]; PRIMGRP[10]:=[ -[1,60,1,"2",[[3,1],[6,1]],1,"A(5)",["A",5,1],[(1,5,7)(2,9,4)(3,8,10),(2,6)(3,5)(4,7)(9,10)]], -[2,120,0,"2",[[3,1],[6,1]],1,"S(5)",["A",5,1],[(1,5,7)(2,9,4)(3,8,10),(1,8)(2,5,6,3)(4,9,7,10)]], +PGAltOnSets(5,2), +PGSymOnSets(5,2), [3,360,1,"2",[[9,1]],2,"PSL(2, 9)",["A",6,1],[(1,2,3)(4,5,6)(7,8,9),(2,4,3,7)(5,6,9,8),(1,10)(4,7)(5,6)(8,9)]], [4,720,0,"2",[[9,1]],3,"PGL(2, 9)",["A",6,1],[(1,2,3)(4,5,6)(7,8,9),(2,6,4,9,3,8,7,5),(1,10)(4,7)(5,6)(8,9)]], [5,720,0,"2",[[9,1]],2,"PSigmaL(2, 9)",["A",6,1],[(1,2,3)(4,5,6)(7,8,9),(2,4,3,7)(5,6,9,8),(4,7)(5,8)(6,9),(1,10)(4,7)(5,6)(8,9)]], @@ -101,8 +101,8 @@ PGSym, ]; PRIMGRP[15]:=[ [1,2520,1,"2",[[14,1]],2,"A(7)",["A",7,1],[(1,4,5)(2,8,10)(3,12,15)(6,13,11)(7,9,14),(1,9,5,14,13,2,6)(3,15,4,7,8,12,11)]], -[2,360,1,"2",[[6,1],[8,1]],1,"A(6)",["A",6,1],[(1,15,7,5,12)(2,9,13,14,8)(3,6,10,11,4),(1,4,5)(2,8,10)(3,12,15)(6,13,11)(7,9,14)]], -[3,720,0,"2",[[6,1],[8,1]],1,"S(6)",["A",6,1],[(1,15,7,5,12)(2,9,13,14,8)(3,6,10,11,4),(1,7)(2,11)(3,12)(4,13)(5,10)(8,14)]], +PGAltOnSets(6,2), +PGSymOnSets(6,2), [4,20160,1,"2",[[14,1]],2,"PSL(4, 2)",["A",8,1],[(1,9,5,14,13,2,6)(3,15,4,7,8,12,11),(1,3,2)(4,8,12)(5,11,14)(6,9,15)(7,10,13)]], PGAlt, PGSym, @@ -167,8 +167,8 @@ PGSym, ]; PRIMGRP[21]:=[ [1,336,0,"2",[[4,1],[8,2]],1,"PGL(2, 7)",["L",[2,7],1],[(1,2)(3,6)(8,15)(9,13)(10,14)(11,12)(16,20)(17,21),(1,19)(2,21)(3,15)(4,20)(5,14)(6,13)(7,17)(11,16)(12,18),(1,7,12,16,19,21,6)(2,8,13,17,20,5,11)(3,9,14,18,4,10,15)]], -[2,2520,1,"2",[[10,2]],1,"A(7)",["A",7,1],[(1,7,12,16,19,21,6)(2,8,13,17,20,5,11)(3,9,14,18,4,10,15),(4,6,5)(9,11,10)(13,15,14)(16,18,17)(19,20,21)]], -[3,5040,0,"2",[[10,2]],1,"S(7)",["A",7,1],[(1,7,12,16,19,21,6)(2,8,13,17,20,5,11)(3,9,14,18,4,10,15),(2,3)(4,5,6)(7,8)(9,10,11)(13,17,15,16,14,18)(19,21,20)]], +PGAltOnSets(7,2), +PGSymOnSets(7,2), [4,20160,1,"2",[[20,1]],2,"PSL(3, 4)=M(21)",["L",[3,4],1],[(1,7,12,16,19,21,6)(2,8,13,17,20,5,11)(3,9,14,18,4,10,15),(2,14,18,20,8)(3,7,12,13,19)(4,21,17,15,10)(5,11,16,6,9)]], PGPsigmaL(3,4), PGPgl(3,4), @@ -261,8 +261,8 @@ PRIMGRP[28]:=[ [4,6048,1,"2",[[27,1]],2,"PSU(3, 3)",["2A",[2,3],1],[(1,4,2,3)(5,21,9,15)(6,19,10,22)(7,16,11,25)(8,26,12,20)(14,27,17,24),(1,7,9)(2,8,10)(3,5,11)(4,6,12)(13,18,14)(15,23,22)(16,28,26)(19,24,25)(20,27,21)]], [5,12096,0,"2",[[27,1]],2,"PGammaU(3, 3)",["2A",[2,3],1],[(1,4,2,3)(5,21,9,15)(6,19,10,22)(7,16,11,25)(8,26,12,20)(14,27,17,24),(1,7,9)(2,8,10)(3,5,11)(4,6,12)(13,18,14)(15,23,22)(16,28,26)(19,24,25)(20,27,21),(1,3)(2,4)(5,7)(6,8)(9,11)(10,12)(15,16)(19,20)(21,25)(22,26)(23,28)(24,27)]], [6,1451520,1,"2",[[27,1]],2,"PSp(6, 2)",["B",[3,2],1],[(2,4,6,8,10)(3,5,7,9,11)(13,20,24,18,15)(14,21,16,22,17)(19,23,25,26,27),(1,12,13,14,15)(3,19,18,17,16)(5,23,22,21,20)(6,27,24,7,10)(8,26,11,25,9),(8,10)(9,11)(14,15)(16,17)(20,21)(26,27),(1,28)(10,11)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)]], -[7,20160,1,"2",[[12,1],[15,1]],1,"A(8)",["A",8,1],[(1,8,14,19,23,26,6)(2,9,15,20,24,5,12)(3,10,16,21,4,11,17)(7,13,18,22,25,27,28),(5,7,6)(11,13,12)(16,18,17)(20,22,21)(23,25,24)(26,27,28)]], -[8,40320,0,"2",[[12,1],[15,1]],1,"S(8)",["A",8,1],[(1,8,14,19,23,26,6)(2,9,15,20,24,5,12)(3,10,16,21,4,11,17)(7,13,18,22,25,27,28),(3,4)(5,6,7)(9,10)(11,12,13)(14,15)(16,17,18)(20,24,22,23,21,25)(26,28,27)]], +PGAltOnSets(8,2), +PGSymOnSets(8,2), PGPsl(2,27), PGPgl(2,27), [11,29484,0,"2",[[27,1]],2,"PSL(2, 27):3",["L",[2,27],1],[(1,2,3)(4,5,6)(7,8,9)(10,11,12)(13,14,15)(16,17,18)(19,20,21)(22,23,24)(25,26,27),(2,4,10,26,9,25,6,16,17,11,20,18,14)(3,7,19,15,5,13,8,22,24,21,12,23,27),(4,11,26)(5,12,27)(6,10,25)(7,21,15)(8,19,13)(9,20,14)(16,18,17)(22,23,24),(1,28)(2,3)(4,27)(5,11)(6,22)(7,14)(8,16)(9,21)(10,23)(12,26)(13,17)(15,20)(18,19)(24,25)]], @@ -322,8 +322,8 @@ PGSym, PRIMGRP[35]:=[ [1,20160,1,"2",[[16,1],[18,1]],1,"A(8)",["A",8,1],[(1,2,4,8,3,6,12)(5,10,15,19,25,29,22)(7,14,18,24,28,34,9)(11,16,20,27,23,13,17)(21,26,32,35,30,31,33),(1,3,7)(2,6,5)(9,10,12)(11,14,13)(16,18,21)(17,22,23)(19,26,24)(25,31,28)(27,33,29)(30,35,32)]], [2,40320,0,"2",[[16,1],[18,1]],1,"S(8)",["A",8,1],[(1,2,4,8,3,6,12)(5,10,15,19,25,29,22)(7,14,18,24,28,34,9)(11,16,20,27,23,13,17)(21,26,32,35,30,31,33),(1,3)(5,6)(9,12)(11,14)(17,23)(18,21)(19,24)(25,31)(27,29)(32,35)]], -[3,2520,1,"2",[[12,1],[4,1],[18,1]],1,"A(7)",["A",7,1],[(1,2,4,8,3,6,12)(5,10,15,19,25,29,22)(7,14,18,24,28,34,9)(11,16,20,27,23,13,17)(21,26,32,35,30,31,33),(2,5,11)(3,7,15)(4,9,10)(6,13,14)(16,21,23)(17,18,22)(19,26,20)(25,30,32)(27,33,34)(28,31,35)]], -[4,5040,0,"2",[[12,1],[4,1],[18,1]],1,"S(7)",["A",7,1],[(1,2,4,8,3,6,12)(5,10,15,19,25,29,22)(7,14,18,24,28,34,9)(11,16,20,27,23,13,17)(21,26,32,35,30,31,33),(2,5)(3,7)(9,10)(13,14)(16,21)(17,22)(19,26)(27,33)(28,31)(30,32)]], +PGAltOnSets(7,3), +PGSymOnSets(7,3), PGAlt, PGSym, ]; @@ -338,8 +338,8 @@ PRIMGRP[36]:=[ [8,25920,1,"2",[[15,1],[20,1]],1,"PSp(4, 3)",["B",[2,3],1],[(2,3,5,10,18)(4,8,15,26,30)(6,12,17,25,22)(7,13,23,24,29)(9,14,19,27,31)(11,20,16,28,34)(21,32,35,33,36),(1,2,4,8,16)(3,6,7,14,25)(5,11,21,32,35)(9,17,18,28,29)(10,19,30,22,33)(12,13,20,24,31)(15,27,34,36,23)]], [9,51840,0,"2",[[15,1],[20,1]],1,"PSp(4, 3):2",["B",[2,3],1],[(2,3,5,10,18)(4,8,15,26,30)(6,12,17,25,22)(7,13,23,24,29)(9,14,19,27,31)(11,20,16,28,34)(21,32,35,33,36),(1,2,4,8,16)(3,6,7,14,25)(5,11,21,32,35)(9,17,18,28,29)(10,19,30,22,33)(12,13,20,24,31)(15,27,34,36,23),(3,7)(4,9)(12,22)(13,24)(14,15)(16,17)(18,29)(19,31)(25,34)(32,35)]], [10,1451520,1,"2",[[35,1]],2,"PSp(6, 2)",["B",[3,2],1],[(1,2,4,8,3,6,12)(5,10,15,19,25,29,22)(7,14,18,24,28,34,9)(11,16,20,27,23,13,17)(21,26,32,35,30,31,33),(1,3)(5,6)(9,12)(11,14)(17,23)(18,21)(19,24)(25,31)(27,29)(32,35),(1,36)(4,23)(6,20)(9,16)(10,21)(13,19)(14,26)(25,34)(27,30)(32,33)]], -[11,181440,1,"2",[[14,1],[21,1]],1,"A(9)",["A",9,1],[(1,2,3,5,7,10,13)(4,6,8,11,15,22,31)(9,12,16,24,17,25,34)(14,20,18,19,28,33,23)(21,30,26,27,35,36,32),(10,14,21)(13,18,26)(15,23,32)(19,27,31)(20,29,30)(24,33,36)(28,35,34)]], -[12,362880,0,"2",[[14,1],[21,1]],1,"S(9)",["A",9,1],[(1,2,3,5,7,10,13)(4,6,8,11,15,22,31)(9,12,16,24,17,25,34)(14,20,18,19,28,33,23)(21,30,26,27,35,36,32),(2,4)(6,9)(10,14,21)(12,17)(13,19,26,31,18,27)(15,23,32)(20,29,30)(22,25)(24,33,36)(28,35,34)]], +PGAltOnSets(9,2), +PGSymOnSets(9,2), [13,259200,0,"4c",[[25,1],[10,1]],1,"(A(6) x A(6)):2",["A",6,2],["4c",[[(2,3,4,5,6),(1,2,3),()],[(1,2,3),(2,3,4,5,6),()],[(),(),(1,2)]]]], [14,518400,0,"4c",[[25,1],[10,1]],1,"(A(6) x A(6)):2^2",["A",6,2],["4c",[[(1,2,3),(2,3,4,5,6),()],[(2,3,4,5,6),(1,2,3),()],[(),(),(1,2)],[(1,2),(1,2),()]]]], [15,518400,0,"4c",[[25,1],[10,1]],1,"(A(6) x A(6)):4",["A",6,2],["4c",[[(1,2,3),(2,3,4,5,6),()],[(2,3,4,5,6),(1,2,3),()],[(1,2),(),(1,2)]]]], @@ -426,8 +426,8 @@ PRIMGRP[45]:=[ [3,1440,0,"2",[[4,1],[16,2],[8,1]],1,"PGammaL(2, 9)",["A",6,1],[(1,2,7)(3,11,27)(4,14,31)(5,18,32)(6,20,36)(8,24,39)(9,25,28)(10,26,42)(12,15,16)(13,30,40)(17,19,21)(22,35,44)(23,33,29)(34,43,37)(38,45,41),(1,3,5,6,7,22,13,23)(2,8,9,10)(4,15,16,17,14,21,19,12)(11,28,29,38,44,25,20,37)(18,33,34,24,40,36,41,39)(26,43,35,32,42,45,27,30),(1,4)(3,12)(5,19)(6,21)(7,14)(8,10)(11,20)(13,16)(15,23)(17,22)(18,33)(24,41)(25,28)(26,43)(27,32)(29,44)(30,35)(34,39)(36,40)(42,45),(3,6)(5,13)(8,10)(11,20)(12,21)(15,17)(16,19)(18,30)(22,23)(24,26)(27,36)(29,44)(32,40)(33,35)(34,45)(37,38)(39,42)(41,43)]], [4,25920,1,"2",[[12,1],[32,1]],1,"PSp(4, 3)",["B",[2,3],1],[(1,3,6,12,19)(2,5,10,18,11)(4,8,15,22,29)(7,14,20,28,40)(9,16,24,33,13)(17,25,34,36,31)(21,30,41,45,32)(23,35,42,37,39)(26,27,38,44,43),(1,2,4,7,13)(3,5,9,14,8)(6,11,15,21,29)(10,17,24,31,19)(12,18,26,37,43)(16,23,34,35,33)(20,27,38,44,40)(22,32,41,45,30)(25,36,42,28,39)]], [5,51840,0,"2",[[12,1],[32,1]],1,"PSp(4, 3):2",["B",[2,3],1],[(1,3,6,12,19)(2,5,10,18,11)(4,8,15,22,29)(7,14,20,28,40)(9,16,24,33,13)(17,25,34,36,31)(21,30,41,45,32)(23,35,42,37,39)(26,27,38,44,43),(1,2,4,7,13)(3,5,9,14,8)(6,11,15,21,29)(10,17,24,31,19)(12,18,26,37,43)(16,23,34,35,33)(20,27,38,44,40)(22,32,41,45,30)(25,36,42,28,39),(7,13)(8,14)(11,18)(12,19)(16,20)(17,26)(21,31)(22,33)(23,32)(24,29)(25,30)(27,39)(28,40)(37,43)(41,42)]], -[6,1814400,1,"2",[[16,1],[28,1]],1,"A(10)",["A",10,1],[(1,2,3,6,9,14,19)(4,7,10,15,12,17,23)(5,8,13,18,24,11,16)(20,26,33,21,28,36,31,38,40,25,32,39,43,45,44,22,29,37,30,35,42)(27,34,41),(2,4)(5,8)(6,10,15,21,28,13,18,23,30,32)(7,11,16,22,29,12,17,19,25,26)(9,14,20,27,35)(24,31,38,43,45)(33,40)(34,36,42,44,41)(37,39)]], -[7,3628800,0,"2",[[16,1],[28,1]],1,"S(10)",["A",10,1],[(1,2,3,6,9,14,19)(4,7,10,15,12,17,23)(5,8,13,18,24,11,16)(20,26,33,21,28,36,31,38,40,25,32,39,43,45,44,22,29,37,30,35,42)(27,34,41),(2,4)(5,8)(6,10,15,21,28,13,18,23,30,32)(7,11,16,22,29,12,17,19,25,26)(9,14,20,27,35)(24,31,38,43,45)(33,40)(34,36,42,44,41)(37,39),(2,5)(4,8)(7,12)(11,17)(16,19)(22,25)(26,29)(33,40)]], +PGAltOnSets(10,2), +PGSymOnSets(10,2), PGAlt, PGSym, ]; @@ -532,8 +532,8 @@ PRIMGRP[55]:=[ [2,1320,0,"2",[[12,4],[6,1]],1,"PGL(2, 11)",["L",[2,11],1],[(1,2,4,8,15,26,41,32,47,13)(3,6,12,21,34,51,37,52,48,36)(5,10,18,31,45,29,44,23,39,25)(7,14,24,40,11,20,35,38,54,50)(9,16,28,43,22)(17,30,19,33,49,46,27,42,53,55),(1,3,7)(2,5,11)(4,9,17)(6,13,23)(10,19,34)(12,22,38)(14,25,26)(15,27,28)(16,29,45)(18,32,48)(20,36,41)(21,37,53)(24,31,46)(30,44,40)(33,50,35)(39,51,49)(42,55,47)(43,52,54)]], [3,1320,0,"2",[[12,1],[24,1],[4,1],[6,1],[8,1]],1,"PGL(2, 11)",["L",[2,11],1],[(1,2,4,8,14,22,34,39,42,44)(3,6,12,18,28,41,52,24,37,48)(5,10,16,25,38,50,27,33,46,31)(7,13,20,30,36)(9,15,23,35,47,54,49,11,17,26)(19,29,43,51,21,32,45,53,55,40),(1,3,7)(2,5,11)(4,9,8)(10,15,24)(12,19,30)(13,21,33)(14,16,18)(17,27,40)(20,31,34)(23,36,35)(25,39,51)(26,28,42)(29,44,52)(37,49,43)(38,45,48)(41,47,50)(53,54,55)]], [4,7920,1,"2",[[36,1],[18,1]],1,"M(11)",["Spor","M(11)",1],[(1,2)(3,4)(6,8)(9,11)(10,13)(12,16)(14,18)(15,20)(17,23)(19,26)(22,29)(24,32)(27,35)(28,37)(30,39)(31,40)(33,42)(34,43)(41,46)(44,45)(47,51)(48,52)(50,53)(54,55),(2,3,5,7)(4,6,9,12)(8,10,14,19)(11,15,21,28)(13,17,24,33)(16,22,30,40)(18,25,34,37)(20,27,36,45)(23,31,41,47)(29,38)(35,44,42,48)(39,46,50,52)(43,49,53,55)(51,54)]], -[5,19958400,1,"2",[[36,1],[18,1]],1,"Alt(11)",["A",11,1],[(1,2,3,5,8,11,15,20,26)(4,6,9,12,16,21,27,33,39)(7,10,13,17,22,28,34,41,47)(14,19,25,32,38,46,29,35,43)(18,24,31,37,45,23,30,36,44)(42,48,49,50,51,52,53,54,55),(2,4,7)(6,10,14)(9,13,18)(12,17,23)(16,22,29)(21,28,26)(27,34,42)(33,40,41)(39,47,48)]], -[6,39916800,0,"2",[[36,1],[18,1]],1,"Sym(11)",["A",11,1],[(1,2,3,5,8,11,15,4,7,10,14)(6,9,12,16,19,18,22,26,31,36,40)(13,17,20,24,23,27,32,37,41,44,47)(21,25,29,28,33,38,42,45,48,50,52)(30,35,34,39,43,46,49,51,53,54,55),(2,4)(3,6)(9,13)(15,18)(17,21)(19,23)(24,28)(25,30)(29,34)]], +PGAltOnSets(11,2), +PGSymOnSets(11,2), PGAlt, PGSym, ]; @@ -543,8 +543,8 @@ PRIMGRP[56]:=[ [3,40320,0,"2",[[45,1],[10,1]],1,"PSL(3, 4).2_1",["L",[3,4],1],[(1,4)(2,35)(3,24)(5,36)(6,20)(7,13)(8,53)(9,25)(10,55)(11,15)(12,42)(14,22)(16,27)(17,38)(19,46)(21,29)(23,45)(26,51)(28,52)(30,34)(31,56)(33,44)(37,41)(39,43)(47,48),(1,49)(2,40,56,17)(3,24,48,52)(4,42,21,10)(6,25,39,28)(7,37)(8,47,38,34)(11,14,55,41)(12,35,27,13)(15,44,18,45)(16,23,54,46)(19,33,26,36)(20,29,53,50)(22,43,31,32)]], [4,40320,0,"2",[[45,1],[10,1]],1,"PSL(3, 4).2_2",["L",[3,4],1],[(1,37)(2,50)(3,52)(4,5)(6,33)(7,44)(8,11)(9,19)(10,31)(12,45)(13,30)(14,36)(15,51)(16,32)(17,25)(18,35)(20,34)(21,26)(22,41)(23,42)(24,56)(27,49)(28,55)(29,53)(38,43)(39,46)(40,54)(47,48),(1,40,51,9,30,27)(2,39,35,10,7,26)(3,21,46,23,33,29)(4,15,25,34,36,32)(5,41,12,22,17,14)(6,38,24,43,53,45)(8,44,55,47,18,11)(13,50,37,48,56,28)(16,54,52,42,19,20)(31,49)]], [5,80640,0,"2",[[45,1],[10,1]],1,"PSL(3, 4).2^2",["L",[3,4],1],[(1,2)(4,6)(7,10)(8,12)(9,13)(14,19)(15,21)(16,22)(17,24)(18,25)(20,28)(23,31)(27,34)(29,37)(33,40)(39,45)(41,48)(42,50)(43,51)(44,53)(49,55),(1,3,5,8,10,15)(2,4,7,11,16,23)(6,9,14,20,29,38)(12,17,22,30,21,25)(13,18,26,33,41,49)(19,27,35,43,52,31)(24,32,39,46,50,55)(28,36,44,53,56,48)(34,42)(37,45,51,40,47,54)]], -[6,20160,1,"2",[[15,1],[30,1],[10,1]],1,"Alt(8)",["A",8,1],[(1,2,4,8,13,19)(3,6,12,18,25,34)(5,10,16,20,27,7)(9,15,22,29,39,48)(11,17,24,32,42,51)(14,21,28,38,47,53)(23,30,40,49,26,36)(31,41,50,55,37,46)(33,43,35,44,52,45)(54,56),(1,3,7)(2,5,11)(4,9,10)(8,14,16)(13,20,28)(15,23,31)(18,26,37)(19,27,22)(24,33,44)(25,35,45)(30,41,38)(32,40,50)(36,46,53)(43,52,47)(49,54,55)]], -[7,40320,0,"2",[[15,1],[30,1],[10,1]],1,"Sym(8)",["A",8,1],[(1,2,3,5,7,11,17,23)(4,6,9,14,21,27,34,42)(8,13,20,26,33,41,48,54)(10,16,18,24,30,38,46,52)(12,19,25,32,40,49,55,56)(15,22,29,36,44,31,39,47)(28,35,43,50,53,37,45,51),(2,4)(5,8)(6,10)(7,12)(9,15)(11,18)(14,20)(21,28)(24,31)(29,37)(35,42)(39,48)(45,50)(46,53)(49,54)]], +PGAltOnSets(8,3), +PGSymOnSets(8,3), PGAlt, PGSym, ]; @@ -705,8 +705,8 @@ PRIMGRP[66]:=[ [1,1320,0,"2",[[5,1],[20,1],[10,4]],1,"PGL(2, 11)",["L",[2,11],1],[(1,2,4,8,14,23,35,53,17,12)(3,6,11,19,5,7,13,22,34,51)(9,16,27,40,52,56,44,60,41,57)(10,18,29,43,59,21,15,25,38,55)(20,32,48,63,31,46,61,30,24,36)(26,39,28,42,58)(33,50,64,37,47,45,49,54,65,66),(1,3,7)(2,5,10)(4,9,17)(6,12,21)(8,15,26)(11,20,33)(13,16,28)(14,24,37)(18,30,45)(19,31,47)(22,29,44)(23,27,41)(25,38,56)(32,49,35)(34,52,43)(36,54,59)(39,57,51)(40,48,50)(42,55,53)(46,62,66)(58,61,65)(60,63,64)]], [2,7920,1,"2",[[15,1],[30,1],[20,1]],1,"M(11)",["Spor","M(11)",1],[(1,2)(3,5)(4,7)(8,11)(9,13)(10,14)(12,17)(15,21)(16,23)(18,26)(19,27)(20,29)(24,32)(25,34)(28,38)(30,41)(31,37)(33,44)(35,42)(36,46)(40,50)(45,54)(47,56)(48,58)(49,59)(52,62)(53,63)(60,65),(1,3,6,9)(2,4)(5,8,12,18)(7,10,15,22)(11,16,24,33)(13,19,28,39)(14,20,30,42)(17,25,35,21)(23,31,43,52)(26,36,47,57)(27,37,48,32)(29,40,38,49)(34,45)(41,51,61,58)(44,53,64,59)(46,55)(50,60)(54,62,66,56)]], [3,95040,1,"2",[[45,1],[20,1]],1,"M(12)",["Spor","M(12)",1],[(1,2)(4,6)(5,8)(7,10)(9,12)(11,15)(13,18)(14,19)(16,22)(17,23)(21,26)(24,29)(25,31)(28,34)(30,37)(33,39)(35,42)(36,43)(38,46)(40,47)(41,48)(44,52)(45,50)(49,56)(51,58)(53,54)(55,57)(59,62)(61,63)(64,66),(1,3,5)(2,4,7)(6,9,13)(8,11,16)(10,14,20)(12,17,22)(15,21,27)(18,24,30)(19,25,32)(23,28,35)(26,33,40)(29,36,44)(31,38,39)(34,41,49)(37,45,53)(42,50,57)(43,51,59)(47,54,61)(48,55,62)(52,60,64)(58,63,65)]], -[4,239500800,1,"2",[[45,1],[20,1]],1,"Alt(12)",["A",12,1],[(1,8,50,9)(2,51,22,60)(3,19)(4,45,27,43)(5,49,61,13)(6,57,55,20)(7,15,30,46)(10,24,11,26)(12,36)(14,63,42,39)(16,58,29,56)(17,33,34,59)(18,41,52,25)(21,47,66,31)(23,32,40,64)(28,65,37,35)(44,48)(54,62),(1,8,12,17,39,22,28,29,9)(2,47,19,14,16,61,65,25,10)(3,31,24,13,58,63,37,18,20)(4,33,53,60,6,27,44,62,59)(5,7,23,32,43,26,35,34,49)(11,36,50,48,52,42,46,54,56)(15,30,45,57,21,41,40,38,64)]], -[5,479001600,0,"2",[[45,1],[20,1]],1,"Sym(12)",["A",12,1],[(1,2,3,4,5,7,10,13,17,21,27,32)(6,9,12,16,20,26)(8,11,14,18,23,22,28,33,38,43,47,51)(15,19,24,30,29,34,39,44,48,52,55,58)(25,31,36,35,40,45,49,53,56,59,61,63)(37,42,41,46,50,54,57,60,62,64,65,66),(4,6)(5,8)(11,15)(17,22)(19,25)(21,26)(23,29)(30,35)(31,37)(36,41)]], +PGAltOnSets(12,2), +PGSymOnSets(12,2), PGAlt, PGSym, ]; @@ -798,8 +798,8 @@ PGSym, PRIMGRP[78]:=[ [1,1092,1,"2",[[14,3],[7,5]],1,"PSL(2, 13)",["L",[2,13],1],[(1,62)(2,65)(3,45)(4,9)(5,74)(6,52)(7,73)(8,10)(11,61)(12,47)(13,75)(14,37)(15,67)(16,34)(17,58)(19,20)(21,41)(22,70)(23,26)(24,64)(25,40)(27,29)(28,68)(31,59)(32,49)(33,66)(35,38)(36,56)(39,43)(42,57)(44,77)(46,63)(48,72)(51,55)(60,71)(69,76),(1,34,65,43,23,21,44,38,16,7,53,72,50)(2,54,46,29,49,14,60,68,9,78,35,66,61)(3,77,18,75,55,8,67,57,10,74,47,30,39)(4,62,69,17,51,70,45,52,5,31,25,73,63)(6,71,20,19,32,22,40,64,42,37,15,56,76)(11,24,41,58,12,48,13,59,26,36,33,27,28)]], [2,2184,0,"2",[[14,5],[7,1]],1,"PGL(2, 13)",["L",[2,13],1],[(2,60)(3,70)(4,67)(5,75)(6,10)(7,64)(8,55)(9,24)(12,63)(14,32)(15,54)(16,36)(17,74)(18,46)(19,78)(20,65)(23,73)(25,34)(26,50)(27,44)(28,47)(29,30)(31,41)(33,53)(35,56)(38,61)(39,59)(40,62)(42,52)(43,76)(45,69)(48,66)(49,57)(68,72)(71,77),(1,7,74,22,76,46,59,3,58,9,40,6,55)(2,50,73,77,39,62,53,35,26,16,48,34,41)(4,37,63,11,78,71,27,65,38,28,32,54,33)(5,15,13,45,12,42,51,44,30,8,10,18,43)(14,25,20,52,67,24,49,60,36,57,70,19,69)(17,61,66,31,47,64,29,23,72,21,68,56,75)]], -[3,3113510400,1,"2",[[22,1],[55,1]],1,"Alt(13)",["A",13,1],[(1,61,59)(2,31,64,51,8,45)(3,53,15,38,24,77,35,68,62,60)(4,73,48,57,74,37)(5,17,20,26,72,9,23,28,70,46,75,49,7,21,30,69,67,25,47,22,6,39,76,66,14,41,42,54,52,36)(10,55,13,11,27)(12,32,50,58,78,63)(16,34,56,65,44,43)(18,40,33,19,29),(1,45,2,73,15,47,76,27,75,13,69,36,32)(3,14,54,66,59,42,77,24,61,25,21,50,53)(4,34,20,38,64,23,11,33,44,49,41,30,31)(5,10,26,43,17,6,60,74,16,28,70,37,35)(7,40,52,67,29,19,46,58,63,56,57,71,8)(9,22,65,51,48,12,68,62,78,18,55,72,39)]], -[4,6227020800,0,"2",[[22,1],[55,1]],1,"Sym(13)",["A",13,1],[(1,2,3,5,7,10,13,17,21,26,31,37,43)(4,6,8,11,14,18,22,27,32,38,44,51,50)(9,12,15,19,23,28,33,39,45,52,58,57,64)(16,20,24,29,34,40,46,53,59,66,65,71,75)(25,30,35,41,47,54,60,67,63,70,74,77,78)(36,42,48,55,61,68,72,49,56,62,69,73,76),(2,4)(6,9)(12,16)(20,25)(30,36)(42,49)(43,50)(51,57)(56,63)(58,65)(66,70)]], +PGAltOnSets(13,2), +PGSymOnSets(13,2), PGAlt, PGSym, ]; @@ -999,8 +999,8 @@ PGAlt, PGSym, ]; PRIMGRP[84]:=[ -[1,181440,1,"2",[[45,1],[18,1],[20,1]],1,"Alt(9)",["A",9,1],[(1,45,37,62,11,56)(2,54)(3,74,79,42,36,35)(4,84,67,43,73,34)(5,28,40,27,83,7)(6,68,53,32,50,69)(8,29,65,25,58,46)(9,18,21,30,20,44)(10,41,51,22,78,60)(13,47,66)(14,24,80,26,76,82)(15,33,38,19,55,77)(16,64,70,48,23,39)(17,61,81,71,63,75)(31,52,57,72,49,59),(1,6,79,77,18,20,22,61,37)(2,58,43,5,8,38,44,17,57)(3,41,9,25,80,35,40,69,53)(4,29,63,11,73,55,24,81,45)(7,31,65,64,21,84,75,78,42)(10,15,12,26,27,50,52,49,68)(13,36,39,47,54,59,67,33,82)(14,19,30,83,32,62,56,70,74)(16,48,76,34,66,72,51,60,28)(23,46,71)]], -[2,362880,0,"2",[[45,1],[18,1],[20,1]],1,"Sym(9)",["A",9,1],[(1,78,24,57,55,63,36,29,81,38,49,20,42,69,12)(2,71,75)(3,21,32,35,82,65,58,17,22,60,9,51,37,26,46)(4,47,27,39,7,80,52,83,30,62,76,40,50,44,66)(5,73,56,13,48,6,14,53,72,18,59,67,28,45,64)(8,41,11,15,68)(10,79,31,25,74)(16,33,54,19,43)(23,34,84,77,70),(1,23,11,9,67,75,47,50)(2,40,37,57,70,8,5,76)(3,73,28,83,62,51,31,81)(4,53,17,69,65,79,13,7)(6,80,56,27,49,36,68,20)(10,14,71,61,52,32,54,16)(12,64,30,29,22,43,19,74)(15,18,44,39,42,34,84,77)(21,72,66,58,45,63,78,59)(24,35,46,33,25,82,55,48)(26,60,38,41)]], +PGAltOnSets(9,3), +PGSymOnSets(9,3), PGPsl(2,83), PGPgl(2,83), PGAlt, @@ -1049,8 +1049,8 @@ PRIMGRP[91]:=[ [2,2184,0,"2",[[12,5],[24,1],[6,1]],1,"PGL(2, 13)",["L",[2,13],1],[(2,27)(3,43)(4,85)(5,51)(7,63)(9,58)(10,78)(12,25)(13,70)(14,87)(15,33)(16,86)(17,84)(18,50)(19,89)(20,36)(21,73)(22,55)(23,82)(24,65)(26,28)(29,35)(31,62)(32,74)(34,90)(37,60)(38,40)(41,72)(42,71)(44,91)(45,61)(46,77)(47,81)(48,68)(49,69)(52,80)(53,66)(54,67)(56,64)(57,79)(59,88)(75,83),(1,11,15,13,21,89,18,91,38,47,34,14,56)(2,63,7,24,32,8,40,59,53,31,50,39,58)(3,60,9,19,86,25,81,74,80,17,55,6,35)(4,45,29,49,57,75,10,51,69,22,42,54,44)(5,30,28,12,16,82,76,79,20,27,48,65,36)(23,73,66,90,26,78,77,84,33,64,43,72,83)(37,87,88,67,71,46,41,61,85,62,70,52,68)]], [3,1092,1,"2",[[12,6],[4,3],[6,1]],1,"PSL(2, 13)",["L",[2,13],1],[(1,86)(2,72)(3,71)(4,77)(5,80)(6,82)(7,90)(8,29)(9,40)(10,11)(12,20)(13,19)(14,85)(15,81)(16,35)(17,27)(18,84)(21,69)(22,32)(23,89)(24,58)(25,53)(26,65)(28,33)(30,38)(31,49)(34,78)(36,55)(37,54)(39,74)(41,42)(43,73)(44,70)(45,46)(47,68)(48,88)(50,63)(51,62)(52,61)(56,59)(57,83)(60,91)(67,87)(75,79),(1,42,61,41,85,29,6,59,4,66,12,7,67)(2,36,74,62,5,76,37,73,70,69,19,72,17)(3,58,83,77,16,46,79,23,28,90,26,56,55)(8,21,87,11,49,32,63,64,35,91,47,71,39)(9,15,14,33,18,34,13,45,38,82,30,40,44)(10,86,43,89,51,78,65,75,81,50,54,48,53)(20,68,24,57,27,60,84,22,52,88,25,31,80)]], [4,2184,0,"2",[[12,2],[24,2],[4,1],[6,1],[8,1]],1,"PGL(2, 13)",["L",[2,13],1],[(1,33)(2,20)(3,45)(4,44)(5,66)(6,36)(8,77)(9,55)(10,43)(11,82)(12,52)(13,35)(15,19)(16,42)(18,54)(21,85)(22,41)(23,90)(24,48)(25,75)(26,53)(27,32)(28,59)(29,76)(30,50)(31,83)(34,74)(37,91)(38,64)(39,89)(40,87)(46,67)(47,65)(49,61)(51,72)(56,84)(57,60)(62,86)(63,70)(68,73)(69,78)(71,79),(1,88,15,34,73,25,63,26,23,11,37,79,62)(2,44,76,39,27,21,54,51,72,13,43,80,55)(3,16,22,67,74,60,50,10,29,68,64,31,69)(4,71,65,89,35,24,59,33,45,57,36,7,75)(5,48,18,83,12,53,32,17,47,49,61,91,58)(6,19,28,40,38,46,84,81,9,30,78,85,70)(8,52,87,66,82,42,86,20,56,14,41,90,77)]], -[5,43589145600,1,"2",[[66,1],[24,1]],1,"Alt(14)",["A",14,1],[(1,73,63,14,85,51,30,53,38,32,76,6,77,22,23,37,59,69,45,49,81,83,72,33,27,68,2,75,41,20,9,13,40,87,35,3,5,91,31,17,7,43,48,28,26)(4,84,29,88,39,55,79,62,64)(8,21,46,44,50,16,56,34,71)(10,70,19,66,25)(11,36,18,89,52,47,54,74,67)(12,58,60,24,42,65,61,90,78)(15,82,80,57,86),(1,28,29,6,48,26,62,25,89,13,44,69,49)(2,34,3,90,7,71,72,20,75,86,56,19,88)(4,77,17,12,14,36,83,24,8,67,9,50,84)(5,87,65,73,37,55,58,81,53,85,74,57,23)(10,61,38,46,82,39,16,64,70,35,21,31,40)(11,63,66,32,45,33,43,30,52,54,76,68,42)(15,47,22,60,80,27,79,41,51,59,18,78,91)]], -[6,87178291200,0,"2",[[66,1],[24,1]],1,"Sym(14)",["A",14,1],[(1,20,82,31,70,60)(2,41,48,65,62,27)(3,64,37,78,76,44)(4,7,71,9,11,68)(5,86,80,33,75,23)(6,25,63,51,74,15)(8,58,39)(10,19,57,40,56,32)(12,85,59,14,72,89)(13,28,77,29,47,17)(16,90,24)(18,55,67)(21,35,83,22,53,36)(26,73,87,69,46,61)(30,38,91,88,79,49)(34,52,54)(42,50,84)(43,45,66),(1,17,75,27,62,15,12,66,61,49)(2,60,55,43,78,89)(3,36,69,88,54,51,8,40,52,46)(4,53,30,64,68,83,63,39,73,81,50,80,44,90,82)(5,20,47,10,74,35)(6,71,59)(7,14,72,87,58,25,84,57,18,41)(9,77,48,34,76)(11,28,13,31,42,19)(16,33)(21,86)(23,79)(24,91,37,67,70)(26,56)(29,38)(45,85)]], +PGAltOnSets(14,2), +PGSymOnSets(14,2), PGPsl(3,9), PGPgammaL(3,9), PGAlt, @@ -1188,8 +1188,8 @@ PRIMGRP[105]:=[ [5,120960,0,"2",[[8,1],[64,1],[32,1]],1,"PSL(3, 4).6",["L",[3,4],1],[(1,55)(2,46)(3,40)(5,50)(7,95)(8,65)(9,33)(10,32)(11,23)(13,62)(14,103)(15,54)(17,78)(18,79)(19,34)(20,82)(21,102)(22,100)(24,31)(25,26)(27,56)(28,84)(29,60)(30,99)(35,43)(36,53)(37,75)(38,69)(39,63)(41,97)(42,66)(44,96)(47,74)(48,101)(49,93)(51,81)(52,83)(57,104)(58,61)(59,70)(64,91)(67,94)(68,89)(71,85)(72,92)(77,86)(87,105)(90,98),(1,65,76)(2,32,78)(3,104,61)(4,14,5)(6,52,84)(7,88,66)(8,38,47)(9,80,74)(10,101,28)(11,100,75)(12,31,59)(13,17,33)(15,83,63)(16,56,77)(18,79,69)(19,30,50)(20,54,68)(21,87,62)(22,58,25)(23,96,24)(26,55,82)(27,85,64)(29,48,42)(34,90,37)(35,51,103)(36,99,105)(39,81,95)(40,102,57)(41,89,91)(43,49,60)(44,53,67)(45,70,94)(46,97,92)(71,86,72)(73,98,93)]], [6,241920,0,"2",[[8,1],[64,1],[32,1]],1,"PSL(3, 4).D_12",["L",[3,4],1],[(1,9,67,72,69,30)(2,6,68,31,61,49)(3,12,7,92,35,36)(4,78,21,32,76,93)(5,43,13,25,66,52)(8,97,27,23,84,20)(10,19,91,46,103,80)(11,55,37,99,48,82)(14,38,101)(15,16,53,39,24,33)(17,83,22,96,45,50)(18,86)(26,34,98,71,77,102)(28,95,65)(29,79,51)(40,90,47)(41,62,105,70,64,74)(42,58)(44,81,59,57,56,60)(54,87,94)(63,100,75)(73,85,89)(88,104),(1,16,4,18,87,83,102,17,89,66)(2,71,101,57,15,80,56,76,53,43)(3,100,81,39,20,64,103,33,40,10)(5,31,32,60,73,93,45,37,90,79)(6,24,22,42,70,98,49,44,75,61)(7,41,62,69,34,94,48,35,85,8)(9,30,59,14,77)(11,67,65,88,47,99,23,84,54,95)(12,19,92,97,58,96,36,82,86,78)(13,51,29,25,46,50,74,63,21,91)(26,105,38,27,68,52,104,28,72,55)]], [7,40320,0,"2",[[12,2],[48,1],[32,1]],1,"Sym(8)",["A",8,1],[(1,2,4,7,11,17,24,34)(3,6,10,15,5,9,13,21)(8,12,19,27,38,52,68,83)(14,22,30,43,59,75,90,49)(16,23,32,45,61,76,84,74)(18,26,36,50,25,35,48,60)(20,29,41,56)(28,40,54,71,88,93,65,80)(31,44)(33,42,58,73)(37,51,66,39,53,70,86,96)(46,63,78,67,82,57,47,64)(55,72,89,98,102,87,95,101)(62,77,91,97)(69,85,94,79)(81,92)(99,103,104,100),(1,3)(2,5)(4,8)(9,14)(10,16)(11,18)(12,20)(17,25)(19,28)(21,30)(22,31)(23,33)(26,37)(27,39)(29,42)(32,46)(34,47)(35,49)(40,55)(41,57)(43,60)(45,62)(48,65)(50,53)(51,67)(52,69)(58,74)(63,79)(64,80)(66,81)(68,84)(70,87)(71,72)(75,77)(76,91)(82,88)(83,93)(85,95)(86,97)(89,99)(92,100)(94,98)(96,102)(101,104)(103,105)]], -[8,653837184000,1,"2",[[78,1],[26,1]],1,"Alt(15)",["A",15,1],[(1,9,4,36,66,57,64)(2,19,89,102,76,65,41)(3,24,93,50,92,56,6)(5,63,46,43,98,45,20)(7,47,26,44,69,53,70)(8,33,59,58,17,90,11)(10,103,84,32,82,29,95)(12,55,79,77,85,67,28)(13,51,105,34,72,71,97)(14,68,75,60,42,87,15)(16,80,91,74,49,83,25)(18,78,40,62,52,39,37)(21,88,100,35,61,99,104)(22,73,96,48,30,101,81)(23,38,54,94,27,31,86),(1,5,95,13,80,94,67,46,40,43,92,88,11,89,17)(2,29,4,23,83,14,38,77,84,44,105,59,28,73,41)(3,35,49,16,78,61,33,52,58,75,54,99,76,56,6)(7,51,22,72,100,81,39,25,103,45,30,55,97,98,91)(8,53,36,47,37,102,26,86,50,32,20,101,48,42,9)(10,68,60,65,71,15,85,64,12,87,24,27,74,104,31)(18,66,34,90,19,63,69,57,62,70,93,21,82,96,79)]], -[9,1307674368000,0,"2",[[78,1],[26,1]],1,"Sym(15)",["A",15,1],[(1,2,3,5,7,10,13,17,21,26,31,37,43,50,57)(4,6,8,11,14,18,22,27,32,38,44,51,58,66,65)(9,12,15,19,23,28,33,39,45,52,59,67,74,73,81)(16,20,24,29,34,40,46,53,60,68,75,83,82,89,96)(25,30,35,41,47,54,61,69,76,84,91,90,97,101,104)(36,42,48,55,62,70,77,85,92,80,88,95,100,103,105)(49,56,63,71,78,86,93,98,64,72,79,87,94,99,102),(2,4)(6,9)(12,16)(20,25)(30,36)(42,49)(56,64)(57,65)(66,73)(72,80)(74,82)(83,90)(88,91)]], +PGAltOnSets(15,2), +PGSymOnSets(15,2), PGAlt, PGSym, ]; @@ -1312,10 +1312,10 @@ PRIMGRP[120]:=[ [15,47377612800,1,"2",[[119,1]],2,"PSp(8, 2)",["B",[4,2],1],[(2,3)(4,6)(5,8)(7,10)(9,11)(15,18)(16,20)(17,22)(21,26)(23,29)(25,32)(27,35)(28,37)(30,40)(31,42)(34,45)(38,50)(39,52)(43,57)(48,55)(49,62)(51,65)(56,70)(60,75)(61,69)(63,79)(64,80)(68,85)(73,83)(74,88)(77,86)(78,93)(84,95)(89,96)(90,97)(100,108)(102,106)(104,111)(107,110)(109,114)(112,116)(113,115)(117,119)(118,120),(1,2,4,7)(3,5,9,12,15,19,25,33)(6,10,13,16,21,27,36,48)(8,11,14,17,23,30,41,55)(18,24,31,43,58,73,90,101)(20,26,34,46,60,76,32,44)(22,28,38,51,66,83,97,105)(29,39,53,68)(35,47,61,77,92,102,108,114)(37,49,63,79,93,80,94,85)(40,54,69,86,99,107,113,118)(42,56,71,88,70,87,75,91)(45,59,74,57,72,89,100,109)(50,64,81,95,103,110,115,119)(52,67,84,98,106,111,116,120)(62,78,65,82,96,104,112,117)]], [16,174182400,1,"2",[[56,1],[63,1]],1,"O+(8, 2)",["D",[4,2],1],[(1,72,82,22,85,78,69,51,114,110,49,74)(2,35,116,108,113,112,5,14,48,41,89,91)(3,94,64,83,71,103,111,73,31,15,98,80)(4,11,56,70,96,50,21,60,12,30,99,39)(6,53,105,88,32,68,66,38,16,102,118,97)(7,115,45,76,61,34,27,33,79,117,119,25)(8,106,77,65,9,62,92,26,81,40,36,37)(10,24,107,44,93,86,90,95,58,59,13,17)(18,28,67,23,29,109,42,104,20,47,19,100)(43,120,63,87,52,101,46,54,57,75,84,55),(1,50,56,14,64)(2,34,22,21,52,70,117,25,18,38,78,84,90,54,9)(3,19,45)(4,101,71,81,98)(5,104,109,110,77,46,16,31,32,39,116,48,12,36,112)(6,114,83,95,119,80,93,60,63,59,41,26,23,44,11)(7,96,102,87,15,24,61,37,8,99,47,27,51,94,57)(10,53,107)(13,108,106,88,33)(17,115,89)(20,58,30,105,97,49,118,67,74,55,43,76,28,85,69)(29,86,75,65,62)(35,68,100,42,120)(40,103,113,79,82)(66,111,92,72,73)]], [17,348364800,0,"2",[[56,1],[63,1]],1,"PSO+(8, 2)",["D",[4,2],1],[(1,53,45,63,57,3,69,19,77,91,35,24)(2,75,10,110,113,70,119,115,48,28,55,32)(4,84,102,68,49,56,18,14,26,8,71,29)(5,46,73,20,82,90,40,108,54,66,103,31)(6,105,106,120,78,85,60,7,117,17,51,107)(9,74,100,12,15,36,50,112,43,61,13,93)(11,16,94,111,47,72,67,39,86,34,104,52)(21,109,118,65,23,92,33,41,25,38,22,87)(27,44,76,42,89,81,83,98,96,97,101,88)(30,95,116,99,80,59,37,62,64,79,58,114),(1,118,107,63)(2,48,19,15,91,29,88,77)(3,33,13,112,9,61,100,117,37,99,86,35,78,51,46,42,96,106,7,68,84,75,21,38)(4,10,69,92,114,59,80,85,14,20,53,79,40,17,11,56,58,55,49,44,72,6,115,81)(5,65,12,52,36,120,25,102,31,108,18,70,22,90,104,27,54,87,116,34,16,32,110,45)(8,109,94,57,47,62,24,39)(23,30,71,103,28,83,113,101)(26,105,76,95)(41,119,82)(43,97,98)(50,73,67,111,64,60)(66,93,89,74)]], -[18,1814400,1,"2",[[35,1],[63,1],[21,1]],1,"Alt(10)",["A",10,1],[(1,55,109,78,66,61,89,84,12)(2,13,6,58,56,68,49,114,59)(3,35,118,105,115,99,117,15,54)(4,93,39,90,83,28,36,73,102)(5,8,10,60,18,75,20,81,97)(7,113,107,116,23,21,82,44,80)(9,57,27,24,47,17,64,25,112)(11,77,45,119,108,76,22,110,72)(14,70,96,40,43,42,52,111,63)(16,37,46,69,100,87,88,32,86)(19,38,65,103,120,104,85,92,41)(26,91,95,74,101,51,94,48,30)(29,62,106)(31,71,53,98,79,34,33,50,67),(1,41,44,14,82,91,90,10)(2,84,20,96,73,80,16,12)(3,4,94,42,113,110,104,71)(5,9,79,69,98,83,47,57)(6,30,29,60,33,67,24,23)(7,119,70,95,92,120,74,100)(8,17,40,53,89,93,72,87)(11,58,61,97,86,68,51,56)(13,46,15,76,28,103,49,112)(18,107,109,114,111,25,78,31)(19,48,43,54,34,66,27,75)(21,88,59,64,32,108,38,65)(22,63,37,36,55,117,106,35)(26,99,116,77)(39,105,62,118,81,101,50,115)(45,52,85,102)]], -[19,3628800,0,"2",[[35,1],[63,1],[21,1]],1,"Sym(10)",["A",10,1],[(1,2,3,4,5,7,9,13,18,24)(6,8,11,15,21,28,38,47,57,30)(10,14,19,26,34,42,53,64,75,84)(12,17,23,31,32,40,50,61,37,46)(16,22,29,39,49,59,70,60,71,80)(20,27,36,44,55,66,77,48,58,68)(25,33,41,52,63,74,83,92,98,102)(35,43,54,65,76,69,79,86,89,94)(45,56,67,78,85,51,62,72,81,88)(73,82,90,95,99,103,106,109,112,115)(87,93,96,100,104,107,110,113,116,118)(91,97,101,105,108,111,114,117,119,120),(4,6)(7,10)(8,12)(11,16)(14,20)(18,25)(22,30)(24,32)(26,35)(27,37)(28,34)(36,45)(38,48)(39,44)(40,51)(49,60)(58,69)(62,73)(71,75)(74,84)(79,87)(81,89)(82,91)(86,92)(90,96)(94,99)(100,105)(102,104)]], -[20,10461394944000,1,"2",[[91,1],[28,1]],1,"Alt(16)",["A",16,1],[(1,86,15,76,118,45,105,72,111,4,103,10,32,75,106,116,63,119,36,17,87,89,66,97,113,33,34,92,42,104,80,57,61,41,52,12,83,35,115,46,109,37,6,68,8,74,13,28,44,73,51,3,85,14,64,69,20,59,90,67,19,21,96)(2,50,24,94,78,56,43)(5,81,23,25,39,120,31,107,38)(7,98,114,70,71,102,79,9,27)(11,26,117,101,29,40,62,65,53)(16,49,18,54,93,84,88,55,47)(22,60,100,91,108,99,110)(30,77,112,82,95,48,58),(1,43)(2,58,36,59,73,69,16,68)(3,67,19,31,107,53,5,38)(4,50,30,44,65,86,12,52)(6,37,9,51)(7,21,15,94,10,32,120,17)(8,85,24,76,118,39,117,27)(11,45)(13,62,102,35,119,33,80,57)(14,26,90,103)(18,34,40,48,115,22,54,109)(20,60,25,77)(23,47,63,99,110,46,93,114)(29,79,55,97,113,61,71,84)(41,70)(42,96,81,108,82,78,98,66)(49,111,72,112,74,95,89,75)(56,87,64,104)(83,91,100,92)(101,116,106,105)]], -[21,20922789888000,0,"2",[[91,1],[28,1]],1,"Sym(16)",["A",16,1],[(1,2,3,5,7,10,13,17,21,26,31,37,43,50,57,65)(4,6,8,11,14,18,22,27,32,38,44,51,58,66,74,73)(9,12,15,19,23,28,33,39,45,52,59,67,75,83,82,90)(16,20,24,29,34,40,46,53,60,68,76,84,92,91,99,107)(25,30,35,41,47,54,61,69,77,85,93,101,100,108,113,117)(36,42,48,55,62,70,78,86,94,102,98,106,112,116,119,120)(49,56,63,71,79,87,95,103,109,81,89,97,105,111,115,118)(64,72,80,88,96,104,110,114),(2,4)(6,9)(12,16)(20,25)(30,36)(42,49)(56,64)(65,73)(72,81)(74,82)(83,91)(89,98)(92,100)(101,106)]], +PGAltOnSets(10,3), +PGSymOnSets(10,3), +PGAltOnSets(16,2), +PGSymOnSets(16,2), PGAlt, PGSym, ]; @@ -1454,8 +1454,8 @@ PRIMGRP[126]:=[ [9,6531840,0,"2",[[45,1],[80,1]],1,"PSU(4, 3).2",["2A",[3,3],1],[(1,72,40,79,107,67,89,60,86,126,8,47)(2,68,75,27,77,73,55,49,34,13,117,52)(3,43,41,31,53,81,123,16,114,23,61,112)(4,101,94,21,58,26,54,12,14,91,95,99)(5,125,65,119,122,93,82,64,121,62,63,9)(6,113,87,17,35,56,97,15,96,66,116,45)(7,11,84,36,38,33,19,98,46,92,24,118)(10,29,105,85,59,111,108,88,90,74,109,22)(18,124,70,37,39,51)(20,83,28,78)(25,42)(30,76,106,69,104,100,48,110,50,115,57,32)(44,102)(71,103,120),(1,93,98)(2,28,40,71,68,6)(3,10,95,79,91,52)(4,92,9,42,73,8)(5,112,99)(7,119,100,115,104,27)(11,94,69,110,108,64)(12,31,85,41,37,124)(13,46,89,47,109,25)(14,30,70,32,43,81)(15,101,17,77,102,50)(16,62,125,24,61,126)(18,58,76,33,53,26)(19,107,21,22,82,67)(20,66,78,113,45,120)(23,103,80,83,114,116)(29,55,117,63,74,86)(34,56,49,35,60,97)(36,123,84,57,111,65)(38,54,59)(39,87,105,96,90,44)(48,121,118)(51,122,88,75,106,72)]], [10,6531840,0,"2",[[45,1],[80,1]],1,"PSU(4, 3).2",["2A",[3,3],1],[(1,10,38,109,115,90,31)(2,101,74,65,98,13,33)(3,39,59,70,60,5,27)(4,91,11,116,14,57,92)(6,110,40,100,47,25,37)(7,75,24,16,97,61,106)(8,111,105,56,123,71,21)(9,20,54,51,29,32,50)(12,121,80,89,66,107,63)(15,35,55,53,67,41,79)(17,18,117,122,28,78,52)(19,96,103,42,114,46,43)(22,48,113,58,82,94,68)(23,102,49,30,73,112,77)(26,126,87,86,69,45,76)(34,108,85,81,104,124,72)(36,83,125,99,84,88,120)(44,93,118,119,62,95,64),(1,18,46,90,61,70,7,105)(2,93,123,4,59,66,110,47)(3,104,55,121,76,31,109,6)(5,115,72,10,35,8,30,75)(9,86,67,27,17,91,54,88)(11,58,98,50,28,106,20,95)(12,44,83,68,100,39,38,49)(13,97,40,23,29,65,21,57)(14,108,113,69,81,34,62,107)(15,26,94,74,119,41,112,52)(16,36,43,92,126,118,79,33)(19,111,53,51,84,22,89,37)(24,77,32,124,78,117,101,102)(25,80,120,42)(45,122,87,63)(48,73,116,114,60,85,82,99)(56,125,96,64)]], [11,13063680,0,"2",[[45,1],[80,1]],1,"PSU(4, 3).2^2",["2A",[3,3],1],[(1,69,23,68,86,90,75,47,100,59)(2,89,88,119,44,91,22,40,5,78)(3,61,114,48,24,29,105,74,14,39)(4,32,115,18,10,57,117,73,19,107)(6,49,76,53,55,17,12,13,111,110)(7,109,121,77,108,37,123,9,101,41)(8,51,21,15,124,85,46,27,35,38)(11,98,87,126,36)(16,118,28,20,56)(25,95,33,63,71)(26,84,99,81,102,34,70,52,60,83)(30,94,54,97,82)(31,62,104,116,112)(42,79,45,106,122,80,43,96,58,64)(50,92,125,103,120)(65,113,67,93,66),(1,32,100,93,27,86,96,31,53,75,38,28,29,117)(2,108,54,13,68,105,36,82,71,25,79,3,17,66)(4,10,47,85,60,43,98,12,73,104,61,110,119,14)(5,72,18,91,64,102,114,70,41,19,20,8,94,50)(6,77,92,101,76,121,49,122,37,63,42,84,115,78)(7,52,103,51,90,89,97,99,80,23,87,30,120,48)(9,65,26,16,88,40,118,109,116,44,22,111,45,46)(11,113,106,123,35,57,125,124,21,33,107,24,34,58)(15,83,69,67,55,62,112,81,95,59,74,39,56,126)]], -[12,181440,1,"2",[[5,1],[60,1],[40,1],[20,1]],1,"Alt(9)",["A",9,1],[(2,41,42)(3,51,106)(4,120,24)(5,121,29)(6,113,57)(7,125,72)(9,16,15)(10,124,23)(11,36,95)(13,21,88)(14,56,103)(18,25,80)(19,28,94)(20,46,52)(22,55,116)(26,39,58)(27,75,100)(31,63,37)(33,40,107)(34,47,117)(35,90,81)(38,60,65)(43,45,91)(44,84,86)(48,62,53)(54,76,71)(59,77,83)(68,79,92)(74,97,87)(82,115,101)(89,102,122)(93,98,111)(96,108,99)(104,105,112)(119,126,123),(1,116,106,20,90,86,88,83,85,65)(2,101,107,51,34,105,19,56,43,21)(3,13,112,115,103)(4,80,54,26,93,119,74,31,35,121)(5,36,37,79,17,57,94,53,61,27)(6,82,48,67,100,98,95,76,68,64)(7,104,124,8,102,14,96,24,16,87)(9,18,125,41,23,118,122,33,108,126)(10,50,69,38,109,110,89,62,49,113)(11,72,59,12,73,114,70,66,22,99)(25,63,39,29,123)(28,40,45,47,42)(30,55,91,46,58,44,117,77,32,60)(52,92,78,75,84)(71,81,111,120,97)]], -[13,362880,0,"2",[[5,1],[60,1],[40,1],[20,1]],1,"Sym(9)",["A",9,1],[(1,2,4,7,11,17,25,35,48)(3,6,10,15,22,32,45,60,76)(5,9,14,20,30,42,56,71,86)(8,13,19,29,40,54,68,84,99)(12,18,27,37,51,65,82,96,110)(16,24,34,28,39,53,67,83,98)(21,31,44,58,74,81,95,109,118)(23,33,46,61,77,90,97,111,119)(26,36,49,50,64,80,93,107,101)(38,52,66,73,88,102,113,117,122)(41,55,69,59,75,89,104,116,114)(43,57,72,87,100,94,108,70,85)(47,63,79,92,106,112,120,124,126)(62,78,91,105,103,115,121,123,125),(1,3)(2,5)(4,8)(7,12)(10,16)(14,21)(15,23)(17,26)(18,28)(27,38)(29,41)(30,43)(31,32)(33,47)(36,50)(44,59)(46,62)(48,52)(55,70)(57,73)(64,81)(65,75)(68,78)(71,85)(80,94)(82,97)(83,84)(87,101)(88,103)(93,104)(96,109)(98,112)(102,114)(107,117)(118,123)]], +PGAltOnSets(9,4), +PGSymOnSets(9,4), [14,976500,1,"2",[[125,1]],2,"PSL(2, 5^3)",["L",[2,125],1],[(1,11,36,90,55,69,104,58,18,5,112,67,41,16,50,28,75,31,102,22,53,15,19,98,27,32,126,122,24,99,21)(2,56,81,91,71,119,68,96,92,60,65,120,73,77,39,70,116,61,17,64,42,76,51,25,106,87,74,34,114,23,37)(3,35,4,13,118,33,125,63,49,8,47,45,84,43,29,93,59,100,79,88,57,89,95,52,108,121,46,97,110,40,123)(6,117,12,72,44,94,83,109,9,124,48,20,80,101,86,115,107,54,66,85,62,10,78,14,82,30,7,26,38,111,103),(1,116,62,61,24,123,115,95,15,56,68,58,34,98,99,87,27,124,33,67,103,20,23,50,46,100,26,112,120,7,101)(2,96,109,117,77,3,57,53,80,83,126,36,70,105,76,16,4,5,69,45,35,47,88,8,114,106,79,42,41,113,102)(6,66,19,25,54,13,121,64,55,12,86,51,93,44,60,18,71,65,104,74,122,11,73,40,111,89,119,75,82,31,81)(10,52,17,91,48,39,108,90,49,78,84,37,97,22,72,21,28,110,14,118,63,30,92,107,29,125,38,32,85,43,59)]], [15,1953000,0,"2",[[125,1]],3,"PGL(2, 5^3)",["L",[2,125],1],[(1,115,83,35,32,71,44,40,19,81,106,52,97,20,112,119,85,8,53,125,24,86,65,61,34,73,70,22,116,104,109,117,62,33,63,55,92,74,59,18,120,27,25,79,23,113,91,5,49,9,41,3,30,17,99,4,47,12,67,108,124,36,57,126,11,76,77,103,60,7,66,95,110,90,89,37,21,84,68,16,15,121,10,39,98,45,2,28,29,94,105,48,69,107,123,38,93,58,101,6,88,75,102,64,96,56,100,14,118,82,26,80,78,111,87,46,31,13,50,42,72,43,114,122),(1,96,6,102,57,87,90,41,53,35,40,120,92,38,94,86,93,42,103,31,4,54,64,73,59,11,50,121,109,52,85,2,8,99,61,112,70,72,107,106,110,89)(3,116,80,18,122,83,43,75,22,104,48,19,56,37,28,68,5,98,119,45,105,95,24,14,74,126,21,114,51,91,82,63,100,71,15,97,44,76,36,123,101,39)(7,58,20,111,117,34,67,10,124,69,108,60,46,55,65,115,88,16,77,26,33,25,81,27,125,79,84,66,78,29,32,62,17,113,23,118,30,9,13,12,47,49)]], [16,2929500,0,"2",[[125,1]],2,"PSigmaL(2, 5^3)",["L",[2,125],1],[(1,94,86,38,107,65,87,67,5)(2,93,24,105,11,17,43,34,72)(3,98,19,51,4,33,69,76,63)(6,58,21,7,124,111,49,103,53)(8,68,125,106,104,112,81,73,115)(9,71,18,35,16,22,31,123,101)(10,41,46,78,45,39,42,88,117)(12,44,29,60,126,52,120,30,96)(13,80,23,89,114,48,110,119,37)(14,113,83,56,59,55,57,91,108)(15,66,50,40,47,79,26,118,100)(20,109,85,84,70,121,61,75,116)(25,97,122,62,36,82,102,90,95)(27,74,54,92,77,32,99,64,28),(1,92,99,119,4,73,64,53,109,97,77,104,31,18,41)(2,102,118,42,16,74,39,44,111,101,43,5,100,105,21)(3,66,90,82,112,23,36,88,49,87,68,7,65,34,60)(6,125,96,94,72,106,115,19,37,83,75,124,85,69,27)(8,61,32,22,29,78,63,50,110,86,12,76,51,59,56)(10,28,17,93,46,113,58,30,47,81,120,80,122,55,25)(11,121,84,95,54)(13,114,67,33,98,91,70,116,14,26,89,52,123,24,126)(15,107,40,79,38,35,57,48,71,108,117,45,62,20,103)]], @@ -1549,8 +1549,8 @@ PRIMGRP[136]:=[ [8,1958400,0,"2",[[60,1],[75,1]],1,"PSp(4, 4).2",["B",[2,4],1],[(1,42,28,93,92,90)(2,118,11,49,114,85)(3,24,97,87,100,20)(4,79,110)(5,16,101,126,30,38)(6,88,29,99,7,107)(8,26,128,105,70,27)(9,46,82)(10,60,74,94,63,23)(13,123,132,51,14,66)(15,125,65,53,81,86)(17,47,96,112,21,73)(18,77,134,50,80,41)(19,52,71,127,45,34)(22,58,36,78,117,37)(25,75,62,61,109,59)(31,108,135,122,55,76)(32,43,103,83,40,136)(33,69,48,39,115,91)(35,130,57,72,133,119)(44,121,54,113,89,64)(56,129,98)(67,102)(68,116,84)(104,124)(106,120),(1,100,132,135,23,51,39,98,79,47)(2,94,114,112,130,56,93,105,34,68)(3,43,126,66,55)(4,57,53,27,54,65,122,120,48,42)(5,113,38,7,74,111,33,21,26,101)(6,37,108,8,69,46,31,131,90,67)(9,119,103,123,10,50,36,125,59,13)(11,70,87,81,63,12,73,129,78,62)(14,96,61,128,75,60,88,80,29,104)(15,91,124,109,17,72,107,45,52,97)(16,99,117,133,85)(18,110,86,32,76)(19,134,58,40,82,25,92,116,95,30)(20,136,64,83,35,71,22,41,84,106)(24,77,115,28,121,44,127,89,118,102)]], [9,197406720,1,"2",[[72,1],[63,1]],1,"O-(8, 2)",["2D",[4,2],1],[(1,114,93,69,107,85,28,72,135,115,31,128,131,119,27,67,102,77,11,83,80)(2,20,88)(3,132,64,133,71,15,98,19,21,86,91,6,7,65,35,24,113,111,58,126,79)(4,16,56,84,108,90,112,25,78,14,123,8,62,104,34,59,89,97,99,51,10)(5,47,13,53,32,74,38,63,43,49,55,12,39,37,100,26,105,136,125,42,46)(9,57,17,33,18,48,52,92,96,118,95,54,40,109,106,70,60,103,75,45,127)(22,50,116,30,82,29,124)(23,134,36,122,44,81,73)(41,120,66,68,101,76,129)(61,130,110,94,87,121,117),(1,49,113,116,58,74)(2,90,130,40,3,29,57,101,100,132,4,34)(5,26,78,22,127,104,108,123,136,43,62,133)(6,135,18)(7,120,36,129,124,39,125,131,81,46,12,64)(8,112,97,41,69,63,117,111,82,19,11,99)(9,92,13,83,103,79,87,17,67,93,38,72)(10,14,55,134,119,107)(15,60,42,44,95,30,32,106,86,33,37,50)(16,91,48,31,121,24)(20,25,51,28,52,84,96,35,109,56,122,47)(21,88,59,80,76,53)(23,128,89,70,77,45)(27,85,126,71,94,115,98,102,68,75,118,66)(54,110,61,114,73,65)]], [10,394813440,0,"2",[[72,1],[63,1]],1,"PSO-(8, 2)",["2D",[4,2],1],[(1,134,116,135,53,6)(2,22,71,36,43,111)(3,82,46,97,4,85)(5,9,108)(7,132,13,94,50,69)(8,107,29,106,55,103)(10,65,18,77,105,61)(11,90,64,67,99,20)(12,54,84,127,49,115)(14,68,41,88,100,120)(15,122,52)(16,34,60,31,38,117)(17,123,119,109,37,70)(19,76,130,131,24,126)(21,110,74)(23,92,26,48,51,95)(25,79,42,35,78,28)(27,101,40,133,63,30)(33,136,86,44,72,56)(39,104,118,96,98,125)(47,62,58,66,124,114)(57,83,112,81,93,75)(59,121)(73,89,113)(91,128)(102,129),(1,31,45,113,41,50,124,125,86,120,36,70)(2,73,76,126,25,75,95,56,34,78,38,94)(3,97,129,81,23,68,57,74,19,46,44,90)(4,40,65,55,47,71,37,22,52,72,14,100)(6,106,133)(7,93,67,16,84,87)(8,79,24,134,109,39)(9,27,49,119,130,96,91,53,17,83,118,35)(10,77,18,60,99,64,117,32,104,105,114,48)(11,128,135,54,26,132,116,62,108,112,89,115)(12,98,58,123,82,30)(13,107,80,66,101,20,121,51,85,43,136,103)(15,63,102,28,29,122)(21,110,88,61,127,111)(33,69,59,92,42,131)]], -[11,177843714048000,1,"2",[[105,1],[30,1]],1,"Alt(17)",["A",17,1],[(1,127,69,20,74,43,72,130,107,90,103,75)(2,135,116,30,100,78)(3,46,98,128,4,22,35,10,119,96,63,14)(5,71,31,85,83,64,17,18,123,50,68,47)(6,112,37,91,73,60,42,136,58,110,121,97)(7,131,59,38,134,9,32,53,133,92,77,27)(8,19,80,61,109,36,48,13,15,114,126,33)(11,76,51,104,16,41,39,70,57,102,21,23)(12,118,44,108,65,111,56,132,88,101,84,52)(25,95,87,40,129,124,26,79,125,99,45,122)(28,105,106,86,115,55,62,89,94,117,113,49)(29,54,67,66,81,34)(82,93,120),(1,41,132,123,66,61,12,3,121,76,43,117,34,35,40,94,78)(2,55,112,58,102,45,23,15,104,46,120,9,127,105,106,85,14)(4,21,39,88,83,22,42,11,65,114,110,89,130,119,68,31,97)(5,100,86,59,37,16,48,27,54,75,36,56,29,136,57,96,108)(6,118,74,50,51,79,8,63,26,44,111,64,17,18,133,128,30)(7,109,33,90,107,73,95,87,70,134,24,72,71,93,92,77,53)(10,91,19,82,131,84,67,115,98,47,80,52,99,60,49,28,122)(13,20,125,135,101,124,103,129,126,38,62,116,81,32,69,25,113)]], -[12,355687428096000,0,"2",[[105,1],[30,1]],1,"Sym(17)",["A",17,1],[(1,2,3,5,7,10,13,17,21,26,31,37,43,50,57,65,73)(4,6,8,11,14,18,22,27,32,38,44,51,58,66,74,83,82)(9,12,15,19,23,28,33,39,45,52,59,67,75,84,92,91,100)(16,20,24,29,34,40,46,53,60,68,76,85,93,102,101,109,118)(25,30,35,41,47,54,61,69,77,86,94,103,111,110,119,125,130)(36,42,48,55,62,70,78,87,95,104,112,117,120,126,131,134,136)(49,56,63,71,79,88,96,105,113,121,99,108,116,124,129,133,135)(64,72,80,89,97,106,114,122,127,81,90,98,107,115,123,128,132),(2,4)(6,9)(12,16)(20,25)(30,36)(42,49)(56,64)(72,81)(73,82)(83,91)(90,99)(92,101)(102,110)(108,117)(111,120)]], +PGAltOnSets(17,2), +PGSymOnSets(17,2), PGAlt, PGSym, ]; diff --git a/data/gps10.g b/data/gps10.g index d47ba7b..078e994 100644 --- a/data/gps10.g +++ b/data/gps10.g @@ -108,8 +108,8 @@ PGAlt, PGSym, ]; PRIMGRP[1001]:=[ 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+PGAltOnSets(14,4), +PGSymOnSets(14,4), PGAlt, PGSym, ]; diff --git a/data/gps11.g b/data/gps11.g index c054a4f..3830f7e 100644 --- a/data/gps11.g +++ b/data/gps11.g @@ -366,8 +366,8 @@ PGAlt, PGSym, ]; PRIMGRP[1035]:=[ 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+PGAltOnSets(46,2), +PGSymOnSets(46,2), PGAlt, PGSym, ]; @@ -664,8 +664,8 @@ PGSym, PRIMGRP[1081]:=[ [1,51888,1,"2",[[48,11],[12,2],[24,22]],1,"PSL(2, 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+PGAltOnSets(47,2), +PGSymOnSets(47,2), PGAlt, PGSym, ]; diff --git a/data/gps12.g b/data/gps12.g index ada3cd8..d267ced 100644 --- a/data/gps12.g +++ b/data/gps12.g @@ -186,8 +186,8 @@ PGSym, PRIMGRP[1128]:=[ [1,51888,1,"2",[[46,13],[23,23]],1,"PSL(2, 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+PGAltOnSets(48,2), +PGSymOnSets(48,2), PGAlt, PGSym, ]; @@ -254,8 +254,8 @@ PGAlt, PGSym, ]; PRIMGRP[1140]:=[ 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+PGAltOnSets(20,3), +PGSymOnSets(20,3), PGAlt, PGSym, ]; @@ -487,8 +487,8 @@ PRIMGRP[1176]:=[ [5,235200,0,"2",[[25,1],[100,9],[50,5]],1,"PGammaL(2, 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+PGAltOnSets(49,2), +PGSymOnSets(49,2), PGAlt, PGSym, ]; @@ -807,8 +807,8 @@ PRIMGRP[1225]:=[ [17,235200,0,"2",[[24,1],[96,10],[48,5]],1,"PGammaL(2, 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+PGAltOnSets(50,2), +PGSymOnSets(50,2), PGAlt, PGSym, ]; @@ -1085,8 +1085,8 @@ PGAlt, PGSym, ]; PRIMGRP[1275]:=[ 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+PGAltOnSets(51,2), +PGSymOnSets(51,2), PGAlt, PGSym, ]; @@ -1169,8 +1169,8 @@ PGAlt, PGSym, ]; PRIMGRP[1287]:=[ 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+PGAltOnSets(13,5), +PGSymOnSets(13,5), PGAlt, PGSym, ]; diff --git a/data/gps14.g b/data/gps14.g index 38ca65f..458f3a7 100644 --- a/data/gps14.g +++ b/data/gps14.g @@ -199,8 +199,8 @@ PGAlt, PGSym, ]; PRIMGRP[1326]:=[ 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+PGAltOnSets(21,3), +PGSymOnSets(21,3), PGAlt, PGSym, ]; @@ -504,8 +504,8 @@ PRIMGRP[1365]:=[ [2,251596800,1,"2",[[320,1],[1024,1],[20,1]],1,"G(2, 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PGPsl(6,4), @@ -731,8 +731,8 @@ PGSym, PRIMGRP[1378]:=[ [1,74412,1,"2",[[54,13],[27,25]],1,"PSL(2, 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+PGAltOnSets(53,2), +PGSymOnSets(53,2), PGAlt, PGSym, ]; diff --git a/data/gps15.g b/data/gps15.g index 57b128c..66f1dc5 100644 --- a/data/gps15.g +++ b/data/gps15.g @@ -195,8 +195,8 @@ PGSym, PRIMGRP[1431]:=[ [1,74412,1,"2",[[52,15],[13,2],[26,24]],1,"PSL(2, 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+PGAltOnSets(54,2), +PGSymOnSets(54,2), PGAlt, PGSym, ]; @@ -570,8 +570,8 @@ PGAlt, PGSym, ]; PRIMGRP[1485]:=[ 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+PGAltOnSets(55,2), +PGSymOnSets(55,2), PGAlt, PGSym, ]; @@ -885,10 +885,10 @@ PGSym, ]; PRIMGRP[1540]:=[ 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+PGAltOnSets(22,3), +PGSymOnSets(22,3), +PGAltOnSets(56,2), +PGSymOnSets(56,2), PGAlt, PGSym, ]; @@ -1227,8 +1227,8 @@ PGSym, PRIMGRP[1596]:=[ 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+PGAltOnSets(57,2), +PGSymOnSets(57,2), PGAlt, PGSym, ]; diff --git a/data/gps16.g b/data/gps16.g index d13d2b0..dd7ff5d 100644 --- a/data/gps16.g +++ b/data/gps16.g @@ -330,8 +330,8 @@ PGAlt, PGSym, ]; PRIMGRP[1653]:=[ 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+PGAltOnSets(58,2), +PGSymOnSets(58,2), PGAlt, PGSym, ]; @@ -886,8 +886,8 @@ PRIMGRP[1711]:=[ [1,102660,1,"2",[[6,1],[10,1],[12,2],[20,4],[60,24],[30,5]],1,"PSL(2, 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+PGAltOnSets(59,2), +PGSymOnSets(59,2), PGAlt, PGSym, ]; @@ -908,8 +908,8 @@ PGAlt, PGSym, ]; PRIMGRP[1716]:=[ 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PGAlt, diff --git a/data/gps17.g b/data/gps17.g index 0616d9f..abe5b03 100644 --- a/data/gps17.g +++ b/data/gps17.g @@ -115,16 +115,16 @@ PGSym, PRIMGRP[1770]:=[ [1,102660,1,"2",[[58,16],[29,29]],1,"PSL(2, 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+PGAltOnSets(60,2), +PGSymOnSets(60,2), PGAlt, PGSym, ]; PRIMGRP[1771]:=[ 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+PGAltOnSets(23,3), +PGSymOnSets(23,3), PGAlt, PGSym, ]; @@ -444,8 +444,8 @@ PGAlt, PGSym, ]; PRIMGRP[1820]:=[ 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+PGAltOnSets(16,4), +PGSymOnSets(16,4), PGAlt, PGSym, ]; @@ -494,8 +494,8 @@ PGSym, PRIMGRP[1830]:=[ [1,113460,1,"2",[[62,15],[31,29]],1,"PSL(2, 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+PGAltOnSets(61,2), +PGSymOnSets(61,2), PGAlt, PGSym, ]; @@ -1030,8 +1030,8 @@ PRIMGRP[1891]:=[ [1,113460,1,"2",[[6,1],[10,1],[12,2],[60,27],[20,4],[30,5]],1,"PSL(2, 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+PGAltOnSets(62,2), +PGSymOnSets(62,2), PGAlt, PGSym, ]; diff --git a/data/gps18.g b/data/gps18.g index 4d81fce..27932bc 100644 --- a/data/gps18.g +++ b/data/gps18.g @@ -322,8 +322,8 @@ PGSym, ]; PRIMGRP[1953]:=[ [1,40317419520,0,"2",[[420,1],[960,1],[60,1],[512,1]],1,"PSL(6, 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+PGAltOnSets(63,2), +PGSymOnSets(63,2), PGAlt, PGSym, ]; @@ -598,8 +598,8 @@ PGAlt, PGSym, ]; PRIMGRP[2002]:=[ 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+PGAltOnSets(14,5), +PGSymOnSets(14,5), PGAlt, PGSym, ]; @@ -710,8 +710,8 @@ PRIMGRP[2016]:=[ [14,50027557148216524800,1,"2",[[1023,1],[992,1]],1,"POmega+(12, 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+PGAltOnSets(64,2), +PGSymOnSets(64,2), PGAlt, PGSym, ]; diff --git a/data/gps19.g b/data/gps19.g index 03b38b0..173c08d 100644 --- a/data/gps19.g +++ b/data/gps19.g @@ -12,8 +12,8 @@ PGSym, ]; PRIMGRP[2024]:=[ 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-[3,3201186852864000,1,"2",[[32,1],[120,1]],1,"Alt(18)",["A",18,1],[(1,35,65,59,113,96,79,36,42,120,95,103,60,67,14)(2,130,66,43,58,136,16,49,141,114,133,146,45,61,30)(3,105,107,108,86,7,9,27,151,71,140,28,89,33,20)(4,125,84,44,93,34,119,13,101,80,83,77,37,116,12)(5,81,18,138,26,152,41,38,10,6,63,142,127,52,126)(8,102,87,94,76,144,64,53,147,90,110,115,51,78,121)(11,55,40)(15,145,68,88,143,47,25,29,124,54,129,21,70,19,72)(17,104,46,91,48,85,97,128,139,148,122,69,74,62,82)(22,109,24,111,137,75,50,98,112,23,92,39,73,32,123)(31,153,56,99,135,131,118,57,117,132,106,149,100,150,134),(1,92,104,79,8,35,125,145,143,86,40,10,30)(2,49,65,89,136,63,18,135,6,112,124,70,14)(3,106,105,11,116,72,25,147,109,16,120,53,148)(4,141,85,5,139,27,142,19,121,81,151,61,12)(7,24,42,102,138,67,47,15,13,111,9,74,38)(17,95,41,76,21,54,22,90,64,114,45,62,48,39,115,71,96,26,28,46,56,100,134,31,34,80)(20,36,101,119,149,99,23,130,29,57,55,126,33)(37,117,118,87,75,127,58,68,88,97,128,122,94,51,98,137,69,66,108,50,52,107,78,131,132,84)(44,77)(59,60)(73,123,144,110,150,83,129,93,140,152,153,91,82)(103,113)(133,146)]], -[4,6402373705728000,0,"2",[[32,1],[120,1]],1,"Sym(18)",["A",18,1],[(1,2,3,5,7,10,13,17,21,26,31,37,43,50,57,65,73,82)(4,6,8,11,14,18,22,27,32,38,44,51,58,66,74,83,92,91)(9,12,15,19,23,28,33,39,45,52,59,67,75,84,93,102,101,110)(16,20,24,29,34,40,46,53,60,68,76,85,94,103,112,111,120,129)(25,30,35,41,47,54,61,69,77,86,95,104,113,122,121,130,138,144)(36,42,48,55,62,70,78,87,96,105,114,123,132,131,139,145,149,152)(49,56,63,71,79,88,97,106,115,124,133,119,128,137,143,148,151,153)(64,72,80,89,98,107,116,125,134,140,100,109,118,127,136,142,147,150)(81,90,99,108,117,126,135,141,146),(2,4)(6,9)(12,16)(20,25)(30,36)(42,49)(56,64)(72,81)(82,91)(90,100)(92,101)(102,111)(109,119)(112,121)(122,131)(128,132)]], +PGAltOnSets(18,2), +PGSymOnSets(18,2), PGAlt, PGSym, ]; @@ -115,8 +115,8 @@ PRIMGRP[165]:=[ [1,13685760,1,"2",[[36,1],[128,1]],1,"PSU(5, 2)",["2A",[4,2],1],[(1,131,40,76,105,63,123,46,49,57,53,84,87,118,38)(2,154,162,109,27,25,8,117,10,41,34,67,54,98,50)(3,161,5,146,68,153,152,73,130,37,78,80,106,48,66)(4,69,72,17,31)(6,136,159,150,120)(7,158,59,143,115)(9,134,116,16,22)(11,119,85,91,97,108,113,127,111,15,32,56,125,126,95)(12,62,88,122,148,70,163,145,18,74,60,99,52,92,83)(13,90,24,139,51,96,77,28,94,65,33,165,147,138,64)(14,164,79,135,100)(19,21,26,30,61,55,160,36,132,140,58,44,141,20,29)(23,45,129,133,137)(35,142,149,89,128)(39,114,101,86,151,112,156,102,43,104,71,47,75,110,144)(42,157,121,124,93)(81,103,82,107,155),(1,61,6,2,88,115)(3,112)(5,165)(7,16)(8,151,75,15,74,82)(9,28,39,139,125,155)(10,69,116,110,40,73)(11,127)(12,35,45,156,160,153)(13,107,91,62,17,84)(14,49,95,19,144,30)(18,55,164,161,26,20)(21,136,22,113,70,108)(23,97)(24,87,93,42,94,98)(25,72,29,111,158,33)(27,51,154,150,83,68)(31,134,78,146,114,90)(32,77,119,48,129,120)(36,121)(37,157)(38,80,135,58,54,118)(41,124,102,105,67,117)(43,71,128,103,106,85)(44,138)(46,56)(47,109)(50,92,148,141,101,133)(52,131,81,99,63,159)(57,137)(59,104)(60,86)(64,143)(65,152,66,76,100,132)(79,149)(89,162)(96,145)(122,142)(130,147)(140,163)]], [2,27371520,0,"2",[[36,1],[128,1]],1,"PGammaU(5, 2)",["2A",[4,2],1],[(1,48,130,5,158,88,64,69,62,8,154,54,149,91,27,143)(2,34,96,76,56,43,126,135,61,29,131,94,83,160,52,121)(3,74,136,148,144,127,114,19,92,113,120,119,55,30,40,104)(4,32,97,77,102,164,112,89)(6,101,152,75,90,31,15,128)(7,42,98,78,103,118,60,140,72,157,36,18,14,139,38,25)(9,129,155,86,163,117,53,20,93,100,82,21,63,106,99,85)(10,125,41,109,67,153,105,33,26,132,51,141,146,122,12,123)(11,142,28,45,17,66,24,108)(13,134,87,137,50,138,35,23,84,150,47,133,65,49,59,22)(16,57,159,151,162,145,46,44,81,70,79,58,73,111,156,110)(37,68,116,80,124,107,165,39)(71,147,95,161),(1,130,113,87,106,7,129,83,114,22,99,67,134,137,162)(2,50,160,69,65,149,64,135,60,27,29,120,86,105,136)(3,46,140,142,36)(4,25,63,131,111)(5,164,17,54,41)(6,110,57,116,139)(8,107,89,31,148)(9,117,85,122,123,58,23,30,78,13,104,73,82,42,81)(10,91,150,95,154,59,79,74,112,100,141,52,56,152,146)(11,159,138,103,26,101,126,14,94,35,77,88,76,49,109)(12,53,24,40,21,143,62,71,133,43,38,72,15,47,121)(16,90,153,161,147,33,66,18,28,80,84,108,157,97,39)(19,158,20,75,32,93,34,127,68,37,151,61,155,165,102)(44,115,70,125,144)(45,132,145,98,55)(48,118,119,96,92)(51,124,163,156,128)]], [3,7920,1,"2",[[12,1],[24,4],[48,1],[8,1]],1,"M(11)",["Spor","M(11)",1],[(1,2)(3,5)(4,7)(6,10)(8,13)(9,15)(11,18)(12,19)(14,22)(16,24)(17,26)(20,30)(21,32)(23,35)(25,38)(27,40)(28,42)(29,44)(31,41)(33,47)(36,51)(37,53)(39,56)(43,59)(45,61)(48,65)(49,66)(50,68)(52,71)(54,73)(55,75)(57,78)(58,80)(60,77)(62,84)(63,86)(64,88)(67,91)(69,76)(70,94)(74,98)(79,89)(81,102)(82,105)(83,104)(85,109)(87,111)(90,114)(92,116)(95,117)(96,118)(97,120)(99,123)(100,125)(101,126)(103,127)(106,121)(108,132)(110,135)(112,137)(115,133)(119,138)(122,144)(124,146)(128,147)(131,142)(136,152)(139,153)(140,141)(143,155)(145,156)(148,151)(149,157)(154,160)(158,162)(163,164),(1,3,6,11)(2,4,8,14)(5,9,16,25)(7,12,20,31)(10,17,27,41)(13,21,33,48)(15,23,36,52)(18,28,43,60)(19,29)(22,34,49,67)(24,37,54,74)(26,39)(30,45,62,85)(32,46,63,87)(35,50,69,93)(38,55,76,44)(40,57,79,102)(42,58,81,104)(47,64,89,113)(51,70,71,95)(53,72,96,119)(56,77,100,94)(59,82,106,130)(61,83,107,131)(65,88,112,138)(66,90,115,140)(68,92,105,129)(73,97,121,127)(75,99,124,126)(78,101,117,142)(80,103,128,148)(84,108,133,125)(86,110,114,139)(98,122,120,143)(109,134,150,144)(111,136)(116,141,154,137)(118,135,151,158)(123,145,147,152)(132,149)(146,157)(153,159,162,160)(155,156,161,163)(164,165)]], -[4,19958400,1,"2",[[56,1],[24,1],[84,1]],1,"Alt(11)",["A",11,1],[(1,7,35,143,120,116,141,158,111)(2,100,114,129,65,132,152,49,160)(3,147,94,118,62,91,113,130,56)(4,34,165,162,57,77,121,63,5)(6,54,41,53,156,27,68,84,142)(8,101,82,83,122,164,136,99,22)(9,20,55,110,125,115,85,32,102)(10,17,87,69,31,150,151,146,138)(11,96,81,46,29,89,112,105,70)(12,144,78,123,16,60,42,92,14)(13,90,40,149,24,106,79,157,104)(15,139,43,38,19,93,154,155,107)(18,76,135,163,159,124,67,23,73)(21,74,98)(25,137,128,86,117,95,108,58,33)(26,119,71,28,52,134,127,148,61)(30,48,131,103,44,39,50,140,47)(36,37,161,133,51,145,80,75,45)(59,126,72,153,66,97,109,88,64),(1,118,28,21,129)(2,86,23,146,157)(3,155,138,128,154)(4,52,68,93,156,33,48,74,165,56)(5,36,6,53,47)(7,37,67,39,150,51,49,161,43,34)(8,134,99,91,29,10,136,111,78,24)(9,110,123,70,14)(12,132,125,95,16,15,122,113,82,13)(17,20)(18,112,35,32,117,22,114,42,26,105)(19,76,124,127,163)(25,73,158,137,61)(27,62,133,79,30,141,57,148,162,40)(31,143,119,106,116)(38,92,107,89,98,46,104,102,94,85)(41,87,140,90,45,152,80,130,103,58)(50,55,131,60,54,164,77,115,84,81)(59,65,126,71,64,159,66,120,72,69)(75,88)(83,97)(96,121)(100,151,160,149,147)(108,109)(135,153)(139,142)(144,145)]], -[5,39916800,0,"2",[[56,1],[24,1],[84,1]],1,"Sym(11)",["A",11,1],[(1,137,125,136,33,55,91,135,86,15)(2,99,122,49,52,70,35,79,76,13)(3,60,163,120,155,9,28,93,143,14)(4,88,39,75,57,84,142,165,41,126)(5,6,77,145,162,103,140,34,59,64)(7,95,18,146,12,124,150,92,110,40)(8,132,148,73,11,23,67,82,134,141)(10,17,128,127,16,25,164,78,69,62)(19,29,46,81,43,65,117,114,118,106)(20,151,152,102,38,144,61,108,138,111)(21,89,31,115,149,83,157,71,129,94)(22,160,96,158,159,105,98,139,100,113)(24,32,85,58,74,104,101,154,90,119)(26,112,116,130,147,123,42,56,87,107)(27,72,45,53,48,97,30,47,80,131)(36,66,54,44,51,121,133,161,109,37)(50,153,156,63,68),(1,130,63,5,64,42,22)(2,106,87,36,156,78,32,128,119,152,47,39,46,112,138,19,90,6,4,85,105)(3,89,129,150,103,43,59,154,102,21,93,80,33,72,157,29,118,74,41,56,66)(7,48,160,8,155,137,76,52,161,61,92,146,100,143,67,51,149,99,86,147,127)(9,117,24,15,65,50,98,70,26,94,95,159,84,91,123,114,107,113,71,77,38)(10,104,111)(11,135,131,132,83,145,134)(12,62,34,116,55,27,151,82,141,165,163,164,162,158,125,79,68,31,60,57,25)(13,108,75,54,110,101,18)(14,17,120,121,69,97,35)(16,139,53,45,81,153,23)(20,148,140,58,88,30,136)(28,115,142,49,109,40,126)(37,122,144,133,124,96,44)]], +PGAltOnSets(11,3), +PGSymOnSets(11,3), PGAlt, PGSym, ]; @@ -232,8 +232,8 @@ PGSym, PRIMGRP[171]:=[ [1,3420,1,"2",[[20,4],[5,2],[10,8]],1,"PSL(2, 19)",["L",[2,19],1],[(1,168)(2,123)(3,76)(4,66)(5,86)(7,153)(8,91)(9,38)(11,55)(12,95)(13,101)(14,71)(15,26)(16,102)(17,99)(18,74)(19,22)(20,72)(21,115)(24,70)(25,28)(27,53)(29,152)(30,109)(31,59)(32,52)(33,83)(34,79)(35,73)(36,93)(37,118)(39,159)(40,160)(41,49)(42,127)(44,121)(45,81)(46,149)(47,51)(48,144)(54,64)(56,131)(57,117)(58,150)(60,112)(61,119)(62,138)(63,80)(65,96)(67,132)(68,171)(69,103)(75,90)(77,111)(78,87)(82,110)(85,104)(88,158)(89,142)(92,151)(94,137)(97,170)(98,116)(100,130)(106,141)(108,154)(113,156)(114,146)(120,124)(122,133)(125,126)(128,145)(134,135)(136,161)(139,163)(140,155)(143,164)(147,167)(157,165)(162,166),(1,56,25,147,12,136,13,140,41,90,129,170,15,63,27,133,160,105,75)(2,26,149,49,100,99,7,31,168,22,122,30,20,57,39,74,85,73,47)(3,71,52,16,130,150,4,97,141,40,33,158,59,152,54,87,120,144,21)(5,106,112,121,157,24,72,9,80,125,58,88,127,53,11,51,70,156,164)(6,78,28,119,153,162,32,45,65,64,114,17,142,101,14,10,137,95,163)(8,62,146,135,50,35,96,145,76,124,98,81,117,84,103,166,110,132,118)(18,44,116,66,48,46,139,79,108,60,86,154,93,94,19,115,83,128,143)(23,155,159,68,165,82,34,43,123,69,134,109,107,36,138,113,151,104,131)(29,77,126,167,169,92,38,37,55,171,148,161,42,111,102,67,89,61,91)]], [2,6840,0,"2",[[20,8],[10,1]],1,"PGL(2, 19)",["L",[2,19],1],[(1,7)(2,122)(3,137)(6,141)(8,78)(9,13)(10,125)(11,171)(12,91)(14,97)(15,116)(16,154)(17,30)(18,29)(19,124)(21,31)(22,41)(23,150)(24,118)(25,117)(26,75)(27,83)(28,44)(33,131)(34,115)(35,43)(36,37)(38,82)(39,123)(42,168)(45,99)(46,164)(47,119)(48,145)(49,120)(50,136)(51,132)(52,84)(53,56)(54,55)(57,121)(59,79)(60,76)(61,67)(62,155)(63,69)(64,68)(66,107)(70,93)(71,92)(72,169)(74,134)(77,149)(80,114)(81,109)(85,156)(86,148)(87,95)(88,163)(89,144)(90,98)(94,112)(96,105)(100,140)(101,110)(102,147)(103,146)(104,166)(108,167)(111,143)(113,162)(127,153)(128,142)(129,160)(130,138)(133,159)(135,152)(139,157)(151,170)(158,165),(1,45,127,30)(2,99,159,109)(3,119,112,132)(4,130,107,155)(5,76,148,94)(6,118,106,93)(7,47,42,67)(8,163,95,165)(9,71,110,170)(10,138,126,140)(11,117,64,44)(12,147,78,154)(13,60,82,137)(14,104,151,113)(15,166,90,156)(16,24,167,36)(17,114,81,69)(18,61,135,51)(19,171,49,54)(20,88,169,157)(21,168,79,153)(22,144,120,128)(23,92,58,97)(25,57,121,28)(26,134,98,29)(27,38,131,101)(31,102,34,108)(32,33,84,53)(35,96)(37,63,70,146)(39,56,122,83)(40,80,129,103)(41,77,124,164)(43,111,73,46)(48,133,142,123)(50,89,161,145)(52,72)(55,62,68,100)(59,74,115,152)(65,75,105,116)(66,160)(85,158,162,139)(86,136)(87,149,91,143)(125,141)]], -[3,60822550204416000,1,"2",[[34,1],[136,1]],1,"Alt(19)",["A",19,1],[(1,132,163,5,47,86,113,168,170,73,115,32,17,87,43,37,61,24,4)(2,123,6,156,55,138,160,128,82,162,135,136,39,77,69,51,78,99,36)(3,16,72,57,141,7,146,74,153,28,161,84,44,45,13,139,140,110,137)(8,81,143,103,11,164,126,76,165,18,104,94,31,22,35,144,130,85,19)(9,12,106,149,158,40,93,92,54,154,147,59,60,53,97,119,120,30,152)(10,131,112,90,116,29,118,52,67,171,15,102,122,95,41,23,68,58,145)(14,63,133,101,148,151,167,26,96,169,108,114,105,46,48,49,150,75,89)(20,83,159,62,21,107,124,88,125,155,80,64,42,66,109,79,33,157,91)(25,111,65,71,34,27,50,134,70,166,142,100,56,127,129,98,38,117,121),(1,112,64,25,102,123,133,91,81,36)(2,142,48,15,131,152,157,121,63,24)(3,8)(6,167,41,7,151,156,149,158,55,14)(9,16)(10,111,65,96,168,146,137,143,92,21)(11,164,163,138,141,47,19,12,159,34)(13,130,147,60,18,114,127,58,169,52)(17,88,161,75,107,134,27,78,42,94)(20,73,116,128,82,106,117,101,126,22)(23,109)(26,61,90,105,32,70,135,85,76,145)(28,170,83,57,113,160,33,30,122,136)(29,98)(35,119)(37,39)(38,46,110,115,45,54,125,95,67,153)(40,166,132,74,165)(43,87)(44,53)(49,140)(50,124,68,97,150,84,77,108,104,66)(51,59)(56,162,154,148,93,103,86,171,72,155)(62,89)(71,79)(80,99)(100,120)(118,129)]], -[4,121645100408832000,0,"2",[[34,1],[136,1]],1,"Sym(19)",["A",19,1],[(1,39,82,74,12,71,134,142,20,26,91,147,111,76,158,159,130,80,168,126)(2,54,160,112,42,135,113,167,6,44,121,162,72,100,169,73,143,62,141,94)(3,88,63,25,27,102,107,164,149,98)(4,18,146,133,23,151,58,8,11,52)(5,109,119,15,40,81,49,161,93,138)(7,55,140,35,170,86,16,29,114,157)(9,69,131,128,47)(10,38,123,13,125,57,14,89,75,24,70,106,36,53,83,117,79,163,78,99,148,33,120,127,166,67,156,19,37,152)(17,104,96,118,41,43,48,108,21,144)(22,51,116,97,45,66)(28,68,64,87,154,50,34,129,60,139)(30,31,103,155,110,95,171,105,132,46,145,65)(32,124,136,150)(56,59,165,84)(61,85,137)(90,153,92,122)(101,115),(1,57,21,80,129,82,36,65,60,35,118,125,25,132,96,63,59,151,91,137,136,119,87,164,120,148,56,157,68,135,9,103,22,142,43,161,16,85,28,2,50,146,100,163,165,24,84,114,49,156,45,15,150,93,81,95,41,121,97,73,140,127,34,99,108,111,133,106,32,3,124,166,112,75,17,8,51,170)(4,66,154)(5,145,10,122,58,27,62,89,168,30,74,52,39)(6,113,33,115,109,169,14,105,88,42,138,38,54)(7,110,128,72,76,55,153,19,92,78,147,98,53)(11,101,117,126,44,29,158,61,162,130,107,47,31)(12,67,40,90,149,160,46,159,134,13,167,37,18)(20,143,86,26,71,141,171,155,94,69,23,79,70)(48,139,104,102,123,116)(64,152,77,131,144,83)]], +PGAltOnSets(19,2), +PGSymOnSets(19,2), PGAlt, PGSym, ]; @@ -357,8 +357,8 @@ PGSym, PRIMGRP[190]:=[ [1,3420,1,"2",[[18,6],[9,9]],1,"PSL(2, 19)",["L",[2,19],1],[(1,61)(2,20)(3,91)(4,58)(5,96)(6,140)(7,33)(8,74)(9,36)(10,64)(11,89)(12,55)(13,122)(14,139)(15,112)(16,178)(17,83)(18,82)(19,131)(21,159)(22,110)(23,113)(24,35)(25,84)(26,134)(27,172)(28,171)(29,49)(30,109)(31,108)(32,76)(34,50)(37,153)(39,62)(40,41)(42,136)(43,71)(44,135)(45,67)(46,115)(47,66)(48,65)(51,86)(52,104)(53,147)(54,100)(56,182)(57,181)(59,69)(60,99)(63,187)(68,145)(70,190)(73,111)(77,97)(78,117)(79,126)(81,98)(85,168)(87,161)(90,189)(92,174)(93,114)(94,105)(95,173)(101,142)(102,176)(103,166)(106,144)(107,121)(116,183)(119,158)(120,184)(123,170)(125,146)(127,165)(128,156)(129,148)(130,154)(133,155)(137,164)(138,162)(141,179)(143,167)(149,177)(151,169)(152,185)(157,175)(160,163)(180,186),(1,157,81,120,147,113,58,7,116,28,25,82,124,95,22,188,111,158,16)(2,39,42,146,162,78,70,182,145,33,106,127,59,174,85,166,175,86,40)(3,144,136,133,105,181,98,8,44,11,93,4,104,55,30,138,103,91,9)(5,84,14,108,121,48,112,29,77,119,27,173,129,63,99,154,123,148,110)(6,71,19,32,160,62,151,180,132,65,88,46,169,117,34,13,177,101,153)(10,80,75,21,79,97,57,137,24,122,60,125,130,76,45,128,52,139,143)(12,96,53,172,94,159,20,167,26,114,149,83,47,131,74,54,126,190,64)(15,23,90,189,184,107,168,156,72,43,69,102,36,152,92,142,150,164,165)(17,171,135,56,61,115,49,31,186,183,41,89,178,66,87,50,38,163,179)(18,185,141,118,161,176,73,37,170,134,35,51,155,109,68,67,100,187,140)]], [2,6840,0,"2",[[36,1],[18,8],[9,1]],1,"PGL(2, 19)",["L",[2,19],1],[(1,78)(2,7)(3,15)(5,165)(6,173)(8,25)(9,167)(10,162)(11,111)(12,129)(13,48)(14,85)(16,64)(17,144)(18,132)(19,121)(20,71)(21,63)(22,128)(23,73)(24,168)(26,117)(27,31)(28,114)(29,106)(30,34)(32,136)(33,43)(35,139)(36,130)(37,182)(38,40)(39,75)(42,137)(44,80)(45,146)(46,156)(47,175)(49,83)(50,70)(51,159)(52,97)(53,96)(54,91)(55,142)(56,69)(57,124)(58,118)(59,153)(60,88)(61,134)(65,176)(66,179)(67,186)(68,79)(72,133)(74,160)(76,164)(77,87)(81,171)(84,163)(86,187)(89,113)(90,95)(92,166)(93,98)(94,116)(100,112)(101,148)(102,122)(103,184)(104,161)(105,185)(107,119)(108,170)(109,190)(110,115)(120,174)(123,172)(125,180)(126,177)(127,147)(131,158)(138,178)(140,189)(141,157)(143,154)(145,149)(150,151)(152,183),(1,129,26,142)(2,113,43,111)(3,49,100,144)(4,93,118,171)(5,69,147,37)(6,149,90,79)(7,86,71,21)(8,32,163,137)(9,123,154,31)(10,107,178,131)(11,97,23,161)(12,127,101,96)(13,54,176,15)(14,41,24,38)(16,51,162,63)(17,77,29,104)(18,151)(19,175,119,179)(20,61,33,117)(22,76,46,42)(25,28,160,98)(27,166,170,120)(30,103,70,174)(34,145,190,126)(35,134,85,78)(36,168,143,139)(39,188)(40,58)(44,57)(45,95,180,140)(47,135,141,80)(48,156,102,110)(50,172,109,108)(52,94,87,152)(53,177,165,68)(55,112,148,91)(56,83,153,106)(59,64,182,138)(60,133)(62,116,75,185)(65,105,122,183)(66,184,157,92)(67,164,125,136)(72,121,155,158)(73,74,89,84)(81,189,114,173)(82,181,132,124)(88,186,99,146)(115,159,128,187)(130,150,167,169)]], -[3,1216451004088320000,1,"2",[[36,1],[153,1]],1,"Alt(20)",["A",20,1],[(1,22,121,19,167,5,124,178,95,92,59,136,141,115,63,169,72,17)(2,159,81,13,110,41,101,14,85,180,175,179,66,94,80,82,68,69)(3,102,47,128,144,32,112,97,37)(4,177,38,29,111,34,145,160,31,164,146,98,174,73,26,182,152,60)(6,186,16,139,105,71,91,119,75,165,137,168,87,131,48,123,33,53)(7,57,170,76,188,50,88,162,183,86,18,166,28,156,10,67,11,135)(8,83,127,39,122,77,142,24,126,55,189,12,117,134,46,147,130,157)(9,190,79,171,113,62,103,84,44,143,104,52,35,133,21,49,30,45)(15,93,40,107,20,96,25,118,70,151,184,140,150,74,54,114,108,58)(23,155,138,100,187,51,109,132,185,106,149,90,176,163,78,99,173,181)(27,42,56,64,36,61,89,153,172,161,65,116,158,125,43,120,154,148),(1,97,37,8,93,41,101,10,85,178,76,164,189,20,66,94,80,82,17)(2,104,60,4,177,45,16,118,89,172,129,171,113,54,103,149,90,125,69)(3,102,28,145,160,31,179,107,6,146,88,174,73,32,112,13,110,119,58)(5,135,11,124,170,95,92,39,122,87,131,141,115,48,123,22,121,14,67)(7,57,180,175,188,128,144,59,136,35,133,77,142,24,126,34,156,19,167)(9,190,70,161,74,71,91,18,155,84,44,143,169,56,163,78,99,185,96)(12,50,109,132,183,117,134,46,147,23,166,130,157,15,83,138,100,187,53)(21,81,33,38,47,86,55,181,40,106,127,26,168,27,72,68,52,63,148)(25,139,105,62,114,29,111,108,75,165,137,176,49,30,51,98,162,173,186)(36,61,79,140,151,153,184,150,65,116,158,182,42,152,43,120,154,159,64)]], -[4,2432902008176640000,0,"2",[[36,1],[153,1]],1,"Sym(20)",["A",20,1],[(1,2,3,5,7,10,13,17,21,26,31,37,43,50,57,65,73,82,91,101)(4,6,8,11,14,18,22,27,32,38,44,51,58,66,74,83,92,102,112,111)(9,12,15,19,23,28,33,39,45,52,59,67,75,84,93,103,113,123,122,132)(16,20,24,29,34,40,46,53,60,68,76,85,94,104,114,124,134,133,143,153)(25,30,35,41,47,54,61,69,77,86,95,105,115,125,135,145,144,154,164,172)(36,42,48,55,62,70,78,87,96,106,116,126,136,146,156,155,165,173,179,184)(49,56,63,71,79,88,97,107,117,127,137,147,157,163,166,174,180,185,188,190)(64,72,80,89,98,108,118,128,138,148,158,167,142,152,162,171,178,183,187,189)(81,90,99,109,119,129,139,149,159,168,175,121,131,141,151,161,170,177,182,186)(100,110,120,130,140,150,160,169,176,181),(2,4)(6,9)(12,16)(20,25)(30,36)(42,49)(56,64)(72,81)(90,100)(101,111)(110,121)(112,122)(123,133)(131,142)(134,144)(145,155)(152,163)(156,166)]], +PGAltOnSets(20,2), +PGSymOnSets(20,2), PGAlt, PGSym, ]; @@ -502,10 +502,10 @@ PGAlt, PGSym, ]; PRIMGRP[210]:=[ -[1,1814400,1,"2",[[24,1],[90,1],[80,1],[15,1]],1,"Alt(10)",["A",10,1],[(1,186,131,2,126,115,107,36,176,111,57,118,108,34,52,125,151,37,123,15,114)(3,73,122,65,181,210,184,124,68,163,88,21,155,170,134,185,117,99,192,205,30)(4,76,166,79,189,105,102,42,63,175,50,190,109,159,25,110,178,69,137,7,11)(5,127,62,95,149,180,64,128,172,194,98,152,92,90,141,16,112,146,10,86,45)(6,157,89,23,9,80,29,145,161,61,93,148,24,17,154,173,48,87,158,38,132)(8,101,144,174,104,164,168)(12,54,47,135,193,66,51,183,204,28,169,46,85,55,22,199,198,208,27,39,70)(13,143,130,177,129,187,103)(14,139,138,142,133,147,140)(18,74,202,106,94,33,206,182,97,196,26,120,19,200,32,75,203,84,96,191,209)(20,82,160,121,59,165,162)(31,153,167,44,119,179,116)(35,49,207,188,78,195,201)(40,83,150,72,91,58,41,136,100,171,71,113,56,60,156,53,81,67,197,77,43),(1,187,72,83,80,184,61,145)(2,24,146,103,5,107,157,207)(3,105,148,181,49,136,43,29)(4,41,106,121,56,122,16,188)(6,82,179,114,81,202,27,62)(7,143,9,22,33,195,156,151)(8,55,110,130,23,140,88,87)(10,91,161,203,100,104,141,101)(11,113,147,54,98,116,182,89)(12,25,78,132,172,26,134,176)(13,15,63,99)(14,115,70,68,185,76,129,144)(17,75)(18,44,94,90,167,197,123,38)(19,40,135,142,158,117,97,47)(20,171,209,102,189,126,205,128)(21,191,201,111,186,163,124,77)(28,42,169,109,174,183,66,60)(30,180,53,210,160,34,118,204)(31,152,64,149,190,150,194,96)(32,86,193,206,133,36,165,69)(35,112,159,45,168,52,175,92)(37,199,164,50,95,79,170,67)(39,208,125,192)(46,196,57,155,153,139,166,71)(48,120,137,173,200,154,138,178)(51,59,65,119,162,93,108,73)(58,177,74,84,127,198,85,131)]], -[2,3628800,0,"2",[[24,1],[90,1],[80,1],[15,1]],1,"Sym(10)",["A",10,1],[(1,2,3,5,8,12,17,24,35,48)(4,7,11,15,22,31,43,53,69,87)(6,10,14,21,29,41,55,71,90,111)(9,13,19,26,38,51,66,82,102,126)(16,23,33,45,60,76,97,119,127,146)(18,25,36,46,61,77,59,75,95,116)(20,28,40,54,70,89,109,133,152,166)(27,39,52,68,85,105,130,150,117,138)(30,42,56,73,67,84,104,96,118,139)(32,44,58,37,50)(34,47,62,78,63,79,98,121,141,157)(49,64,80,100,124,144,161,163,176,185)(57,74,93,86,106,131,65,81,101,125)(72,91,112,135,145,162,175,177,186,193)(83,103,128,147,158,170,180,188,194,199)(88,108,122,142,159,171,114,137,156,169)(92,113,136,155,120,140,148,164,172,182)(94,115,107,132,151)(99,123,143,160,173,183,190,196,201,205)(110,134,153,167,178,181,189,195,200,204)(129,149,165,174,184,191,197,202,206,208)(154,168,179,187,192,198,203,207,209,210),(2,4)(3,6)(5,9)(11,16)(12,18)(13,20)(19,27)(21,30)(22,32)(23,34)(25,37)(33,46)(35,49)(39,53)(42,57)(44,59)(48,63)(50,65)(51,67)(55,72)(61,76)(66,83)(68,86)(69,88)(70,71)(73,92)(74,94)(75,96)(79,99)(85,100)(87,107)(89,110)(93,114)(95,117)(97,120)(98,122)(101,119)(102,127)(103,129)(116,130)(121,133)(124,145)(128,148)(134,154)(139,144)(141,158)(143,153)(146,163)(159,172)(160,174)(164,177)(170,181)(180,185)(182,183)(184,192)(191,193)]], -[3,25545471085854720000,1,"2",[[38,1],[171,1]],1,"Alt(21)",["A",21,1],[(1,66,187,188,123,77,203,192,100,51,158,205,4,104,135,145,169,119,166,91,64,68,210,160,121,50,201,167,146,84,122,103,16,131,101,183,81,87,197,149,180,108,144,82,157,154,147,202,9,148,207,172,49,59,190,114,25,142,124,92)(2,83,185,6,125,34,55,204,32,38,107,54,99,93,174)(3,102,139,72,129,62,89,136,28,63,173,116,110,57,7)(5,177,198,21,27,39,31,67,130,15,178,73,168,179,163)(8,196,113,56,106,23,71,171,96,40,35,138,105,176,152)(10,120,184,94,30,75,14,109,208,60,33,69,46,37,118,88,24,115,162,132,140,98,19,159,22,52,13,44,61,58)(11,155,161,128,42,95,79,153,206,48,150,151,90,85,141)(12,175,195,41,191,17,26,53,76,70,164,193,189,156,65)(18,80,127,74,20,186,200,194,133,117,47,29,182,45,86)(36,43,209,137)(97,181,199,143)(111,126)(112,134,165,170),(1,170,200,164,198,54,27,89,92)(2,101,138,86,41,205,49,51,185)(3,91,100,68,5,167,123,59,47)(4,148,62,63,177,160,81,131,202)(6,112,146,50,34,15,204,31,128)(7,35,171,116,72,166,82,180,77)(8,155,182,26,55,188,134,165,119)(9,126,16,142,195,80,191,71,172)(10,129,37,162,179,181,184,57,60)(11,192,121,84,12,144,102,76,21)(13,85,94,30,147,115,118,117,88)(14,186,159,46,106,109,199,169,43)(17,70,151,110,135,156,158,161,130)(18,53,105,168,122,124,93,96,28)(19,103,143,97,163,120,208,95,52)(20,210,127,74,56,201,173,67,139)(22,152,69,61,65,132,209,83,58)(23,99,113,90,203,196,114,64,108)(24,125,44,33,175,137,36,66,98)(25,87,79,189,133,197,150,153,183)(29,149,157,154,187,178,136,32,40)(38,194,145,111,104,141,48,206,39)(42,190,73,176,207,193,107,45,174)(75,78,140)]], -[4,51090942171709440000,0,"2",[[38,1],[171,1]],1,"Sym(21)",["A",21,1],[(1,2,3,5,7,10,13,17,21,26,31,37,43,50,57,65,73,82,91,101,111)(4,6,8,11,14,18,22,27,32,38,44,51,58,66,74,83,92,102,112,123,122)(9,12,15,19,23,28,33,39,45,52,59,67,75,84,93,103,113,124,134,133,144)(16,20,24,29,34,40,46,53,60,68,76,85,94,104,114,125,135,146,145,155,166)(25,30,35,41,47,54,61,69,77,86,95,105,115,126,136,147,157,156,167,177,187)(36,42,48,55,62,70,78,87,96,106,116,127,137,148,158,169,168,178,188,195,201)(49,56,63,71,79,88,97,107,117,128,138,149,159,170,180,179,189,196,202,206,209)(64,72,80,89,98,108,118,129,139,150,160,171,181,165,176,186,194,200,205,208,210)(81,90,99,109,119,130,140,151,161,172,182,190,143,154,164,175,185,193,199,204,207)(100,110,120,131,141,152,162,173,183,191,197,121,132,142,153,163,174,184,192,198,203),(2,4)(6,9)(12,16)(20,25)(30,36)(42,49)(56,64)(72,81)(90,100)(110,121)(111,122)(123,133)(132,143)(134,145)(146,156)(154,165)(157,168)(169,179)(176,180)]], +PGAltOnSets(10,4), +PGSymOnSets(10,4), +PGAltOnSets(21,2), +PGSymOnSets(21,2), PGAlt, PGSym, ]; @@ -585,8 +585,8 @@ PGSym, ]; PRIMGRP[220]:=[ [1,95040,1,"2",[[12,1],[27,1],[72,1],[108,1]],1,"M(12)",["Spor","M(12)",1],[(1,2)(3,5)(4,7)(6,10)(8,11)(9,12)(13,17)(14,18)(15,20)(16,22)(19,26)(21,28)(23,30)(24,31)(25,33)(27,35)(29,38)(32,42)(34,44)(36,45)(37,46)(39,49)(40,50)(41,52)(43,55)(47,60)(48,61)(51,65)(53,67)(54,68)(56,71)(57,72)(58,73)(59,75)(62,79)(63,80)(64,82)(66,85)(69,81)(70,89)(74,94)(76,95)(77,96)(78,98)(83,103)(84,104)(86,107)(87,108)(88,110)(90,113)(91,114)(92,116)(93,118)(97,122)(99,101)(100,123)(102,126)(105,129)(106,130)(109,133)(111,135)(112,125)(115,139)(117,141)(119,143)(120,144)(121,140)(124,148)(127,150)(128,147)(131,154)(132,155)(134,157)(136,160)(137,161)(138,162)(142,166)(145,156)(146,170)(149,172)(151,173)(152,174)(153,176)(158,181)(159,182)(163,185)(164,187)(165,168)(167,188)(169,190)(171,189)(175,196)(177,197)(178,198)(179,199)(180,200)(183,193)(184,195)(186,203)(191,206)(192,207)(194,201)(202,212)(204,213)(205,214)(208,217)(209,218)(210,219)(211,220)(215,216),(1,3,6)(2,4,8)(5,9,13)(10,14,19)(11,15,21)(12,16,23)(17,24,32)(18,25,34)(20,27,36)(22,29,39)(28,37,47)(30,40,51)(31,41,53)(33,43,56)(35,44,57)(38,48,62)(42,54,69)(45,58,74)(46,59,76)(49,63,81)(50,64,83)(52,66,86)(55,70,90)(60,77,97)(61,78,99)(65,84,105)(67,87,109)(68,88,111)(71,91,115)(72,92,117)(73,93,119)(79,100,124)(80,101,125)(82,102,127)(85,106,131)(89,112,136)(94,120,145)(95,108,132)(96,121,146)(98,122,147)(103,114,138)(104,128,151)(107,113,137)(110,134,158)(116,140,164)(118,142,167)(123,126,149)(129,152,175)(130,153,177)(133,156,179)(135,159,183)(139,163,186)(141,165,181)(143,168,189)(144,169,191)(148,171,150)(154,155,178)(157,180,188)(160,184,202)(161,170,192)(162,174,195)(172,193,208)(173,194,209)(176,196,198)(182,201,212)(185,187,204)(190,205,199)(197,210,213)(200,211,218)(203,206,215)(207,216,219)(214,217,220)]], -[2,239500800,1,"2",[[27,1],[84,1],[108,1]],1,"Alt(12)",["A",12,1],[(1,2,4,7,11,15,22,31,45,66)(3,5,8,12,17,25,36,52,74,102)(6,10,13,19,28,41,60,87,103,131)(9,14,21,30,43,63,91,118,143,160)(16,23,33,48,62,89,115,142,32,46)(18,27,39,57,82,111,137,155,171,188)(20,29,42,61,88,114,141,159,176,193)(24,35,51,73,90,117,133,148,47,68)(26,38,55,79,53,76,105,121,49,70)(34,50,71,99,127,149,165,183,199,212)(37,54,77,107,135,153,169,186,202,213)(40,58,84,113,92,119,144,161,177,98)(44,64,93,101,129,65,95,123,72,100)(56,80,109,83,112,138,156,172,189,205)(59,86,106,134,120,146,162,179,194,126)(67,96,124,145,163,181,197,180,196,211)(69,97,125,139,157,174,191,208,218,210)(75,104,132,152,168,185,201,206,216,85)(78,108,136,154,170,187,203,214,81,110)(94,122,147,164,182,198,173,190,207,217)(116,140,158,175,192,209,219,204,215,220)(128,150,166,130,151,167,184,200,178,195),(1,3,6)(5,9,10)(8,13,20)(11,16,24)(12,18,19)(17,26,28)(22,32,47)(23,34,35)(25,37,41)(27,40,59)(30,44,65)(33,49,51)(36,53,60)(38,56,81)(42,62,90)(46,67,68)(48,69,73)(50,72,101)(52,75,87)(54,78,109)(57,83,108)(58,85,86)(63,92,120)(64,94,95)(70,98,126)(74,103,88)(76,106,84)(79,110,80)(89,116,117)(93,121,123)(100,128,129)(102,130,131)(105,133,115)(112,139,136)(113,140,134)(119,145,146)(122,148,142)(138,154,149)(144,162,180)(156,173,170)(161,178,179)(172,187,204)(177,194,210)(189,206,203)(205,214,213)]], -[3,479001600,0,"2",[[27,1],[84,1],[108,1]],1,"Sym(12)",["A",12,1],[(1,2,4,7,10,15,23,33,31,42,52,63)(3,6,9,14,21,30,41,51,35,45,55,27)(5,8,12,18,26,37,47,58,68,79,91,105)(11,17,25,36,46,57,67,77,89,86,99,113)(13,20,29,39,49,60,71,82,95,109,124,138)(16,24,34,44)(19,28,38,48,59,70,81,93,107,121,114,129)(22,32,43,54,65,53,64,74,62,73,85,98)(40,50,61,72,84,69,80,92,106,120,56,66)(75,87,100,115,130,143,97,111,126,140,153,165)(76,88,102,117,132,145,83,96,110,125,139,152)(78,90,103,118,133,146,112,127,141,154,166,177)(94,108,122,136,147,160,128,142,155,167,178,187)(101,116,131,144,157,158,170,181,190,197,203,209)(104,119,134,148,161,156,168,179,188,195,201,207)(123,137,150,162,173,159,171,182,191,198,204,210)(135,149,163,174,169,180,189,196,202,208,213,216)(151,164,175,185,172,183,192,199,205,211,214,217)(176,186,194,184,193,200,206,212,215,218,219,220),(1,3)(2,5)(7,11)(8,13)(10,16)(12,19)(14,22)(18,27)(21,31)(24,35)(29,40)(42,53)(45,56)(50,62)(57,68)(58,69)(64,75)(66,76)(67,78)(70,82)(71,83)(73,86)(81,94)(84,97)(87,101)(90,104)(98,112)(99,114)(100,102)(108,123)(113,128)(115,118)(119,135)(131,134)(133,147)(137,151)(143,156)(145,158)(146,159)(148,162)(157,169)(161,172)(163,175)(164,176)(174,184)]], +PGAltOnSets(12,3), +PGSymOnSets(12,3), PGAlt, PGSym, ]; @@ -673,8 +673,8 @@ PGSym, PRIMGRP[231]:=[ [1,443520,1,"2",[[160,1],[40,1],[30,1]],1,"M(22)",["Spor","M(22)",1],[(2,154)(3,4)(5,184)(6,22)(7,167)(8,139)(9,55)(10,75)(11,122)(13,114)(14,126)(16,87)(17,166)(18,162)(19,79)(20,50)(21,230)(23,145)(24,229)(25,201)(26,226)(27,118)(28,89)(29,152)(30,120)(31,41)(32,200)(33,156)(34,71)(35,53)(36,102)(38,107)(39,128)(40,62)(42,86)(44,220)(45,67)(46,115)(47,105)(48,148)(49,91)(52,69)(56,78)(57,158)(58,205)(59,68)(60,119)(61,192)(63,160)(64,65)(70,134)(73,182)(74,197)(76,227)(77,164)(80,170)(81,117)(82,104)(83,193)(85,210)(88,123)(90,216)(92,142)(94,180)(95,132)(96,198)(97,185)(98,176)(101,187)(106,136)(108,203)(109,222)(110,188)(111,157)(112,129)(113,150)(121,196)(124,177)(125,131)(127,141)(130,151)(133,165)(135,159)(137,186)(138,228)(143,217)(146,204)(147,211)(149,161)(153,218)(155,190)(163,213)(168,179)(169,191)(171,223)(172,221)(173,214)(174,209)(175,189)(183,202)(194,231)(195,225)(199,224)(206,212),(1,48,61,67)(2,206,89,3)(4,93,77,228)(5,178,194,17)(6,173,40,83)(7,168,174,28)(8,213,214,15)(9,158,112,204)(10,124,180,50)(11,97,221,70)(12,56,26,64)(13,65,176,230)(14,159,163,144)(16,162,184,147)(18,115,175,96)(19,33,29,143)(20,108,94,216)(21,141,130,69)(22,148,54,190)(23,78,140,36)(24,209,74,215)(25,95,106,161)(27,84,44,188)(30,187,218,193)(31,85,137,121)(32,133)(34,81,212,225)(35,107)(37,41,57,172)(38,205,134,196)(39,231)(42,177,136,217)(43,88,126,154)(45,92,105,119)(46,185)(47,113,183,151)(49,62,103,219)(51,111)(52,165,63,207)(53,181,198,76)(55,118,101,72)(58,155,86,222)(59,182,200,80)(60,203,82,171)(66,117,220,179)(68,153,157,71)(73,169,170,99)(75,114,156,122)(79,197,224,125)(87,132)(90,223)(91,123,226,195)(98,128,186,149)(100,135)(102,104,150,229)(109,160,202,127)(116,201,167,210)(120,139,164,129)(131,146,142,208)(138,227,191,166)(145,211)(189,192)]], [2,887040,0,"2",[[160,1],[40,1],[30,1]],1,"M(22).2",["Spor","M(22)",1],[(1,2)(4,7)(5,9)(6,12)(8,15)(10,19)(11,22)(13,26)(14,28)(16,32)(17,34)(18,21)(20,38)(23,40)(24,42)(25,45)(27,47)(29,51)(30,37)(31,56)(33,59)(35,63)(36,66)(39,71)(43,77)(44,72)(46,81)(48,84)(49,86)(50,80)(52,92)(53,94)(55,89)(57,99)(58,101)(60,98)(61,103)(62,106)(64,109)(65,110)(67,113)(68,115)(69,118)(70,120)(73,100)(74,126)(75,128)(76,131)(78,133)(79,95)(82,87)(83,117)(85,140)(88,144)(90,146)(91,147)(96,151)(97,152)(102,123)(105,130)(107,161)(111,124)(112,116)(114,168)(121,176)(122,178)(125,183)(127,184)(132,166)(134,181)(135,193)(136,174)(137,195)(139,148)(141,197)(142,198)(143,199)(145,173)(149,204)(150,202)(153,206)(154,158)(155,207)(156,159)(157,188)(162,211)(163,212)(167,203)(169,214)(170,216)(171,217)(172,208)(175,219)(177,194)(185,215)(187,205)(189,190)(191,209)(192,221)(201,227)(213,218)(222,231)(225,228)(229,230),(1,3,6,13)(2,5,10,20)(4,8,16,33)(7,11,23,41)(9,17,35,64)(12,24,43,25)(14,29,52,93)(15,30,54,58)(18,28,49,87)(19,37,68,116)(22,39,72,123)(26,46,66,112)(27,48)(31,55,97,153)(32,57,100,155)(34,61,104,158)(36,67)(38,70,121,177)(40,74,127,186)(42,75,129,161)(44,78)(45,79)(47,83,126,185)(50,89,81,114)(51,90,84,138)(53,95,60,85)(56,98,147,201)(59,102)(62,107,162,173)(63,108,163,157)(65,111,167,135)(69,119,174,218)(71,122,179,193)(73,125,184,214)(76,132,190,195)(77,96,115,170)(80,134,101,156)(82,136,194,225)(86,141,164,91)(88,143,197,154)(92,148,120,175)(94,149,198,217)(99,145,200,166)(103,142,181,221)(105,159,209,199)(106,160,210,204)(110,165)(113,168,213,231)(117,124,182,139)(118,172,151,205)(128,187,137,180)(130,189)(131,140,196,226)(133,191,188,223)(144,146,152,150)(169,215)(171,208)(176,178,212,219)(183,206,220,229)(192,224,227,203)(202,211)(216,230,228,222),(1,4)(5,11)(6,14)(9,18)(10,21)(12,25)(13,27)(15,31)(17,36)(19,22)(20,23)(24,44)(28,50)(29,53)(30,55)(32,58)(33,60)(34,62)(35,65)(37,69)(39,73)(42,76)(43,78)(45,80)(46,82)(48,85)(49,88)(51,91)(54,96)(57,77)(61,105)(63,90)(64,106)(66,109)(67,114)(68,117)(71,107)(72,124)(75,130)(79,120)(81,135)(83,137)(84,139)(86,142)(87,143)(89,145)(94,150)(97,100)(99,154)(102,127)(103,157)(108,164)(110,166)(111,131)(112,136)(113,169)(115,171)(116,125)(118,173)(119,138)(121,156)(122,180)(123,181)(126,162)(128,188)(129,149)(132,146)(133,158)(134,192)(140,167)(141,182)(144,189)(147,202)(148,203)(151,179)(152,161)(153,170)(155,208)(160,197)(163,174)(165,210)(168,213)(172,191)(175,177)(178,220)(183,212)(184,221)(185,222)(190,198)(193,199)(195,217)(196,200)(204,226)(205,228)(207,229)(209,230)(214,218)(215,231)]], -[3,562000363888803840000,1,"2",[[190,1],[40,1]],1,"Alt(22)",["A",22,1],[(1,77,211,141,150,9,104,62,13,174,25,143,12,22,112,194,51,5,187,162,49,68,7,24,169,64,172,165,61,212,170,59,23,33,216,4,155,34,230,103,121,131,209,46,198,81,108,8,30,186,134,66,79,19,82,100,87,47,10,192)(2,56,221,148,85,89,217,139,39,27,40,15)(3,181,32,226,106,70)(6,163,206,129,38,11,204,90,17,214,153,99)(14,208,158,167,119)(16,97,223,36,126)(18,63,20,48,145,117,196,177,127,71,175,26)(21,224,189,110,41,124,95,53,55,199,80,42)(28,168,201,45,191,83,31,29,151,54,35,72)(37,109,115,44,69,52,88,120,132,60,184,75)(43,98,78,138,144)(50,202,118,135,190,195,142,228,114,122)(57,213,154,147,76,231,86,218,166,133,96,111)(58,205)(65,105,200,73,116,152,128,176,210,193,140,136)(67,179,93,220,107,225,130,156,178,229,160,171)(74,159)(84,188,164,92,182)(91,146,149,219,222)(101,125,173,203,102,185,215,197,227,180,157,207)(123,137),(1,128,50,211,70,3,157,151,87,34,218,189,132,26,97,223,25,210,178,214,51,5,227,204,42,21,195,165,88,80,30,174,167,188,130,168,110,55,149,209,18,48,133,106,43,62,10,192)(2,72,68,119,7,15)(4,193,86,172,79,11,180,181,27,77,202,153,120,90,33,126,16,176,166,145,38,131,219,199,35,56,225,66,98,54,24,169,81,84,142,224,99,6,197,104,23,28,156,201,52,59,14,216)(8,20,63,155,47,108)(9,113,93,226,45,179,125,115,39,22,135,194,94,76,230,150)(12,40,143)(13,186,122,65,58,206,61,212,146,73,107,221,213,177,161,139)(17,229,171,75,44,46,208,158,182,74,160,196,89,203,102,175)(19,91,170,152,96,111,85,109,185,187,198,64,159,57,184,31)(29,207,147,129,60,220,141,138,100,164,114,134,105,154,101,127)(32,228,103,144,116,118,112,121,200,137,124,53,41,123,83,69)(36,92,190,136,67,191,173,217,215,163,231,117,205,95,78,162)(37,71,222,82,49,140,183,148)]], -[4,1124000727777607680000,0,"2",[[190,1],[40,1]],1,"Sym(22)",["A",22,1],[(1,2,3,5,7,10,13,17,21,26,31,37,43,50,57,65,73,82,91,101,111,122)(4,6,8,11,14,18,22,27,32,38,44,51,58,66,74,83,92,102,112,123,134,133)(9,12,15,19,23,28,33,39,45,52,59,67,75,84,93,103,113,124,135,146,145,156)(16,20,24,29,34,40,46,53,60,68,76,85,94,104,114,125,136,147,158,157,168,179)(25,30,35,41,47,54,61,69,77,86,95,105,115,126,137,148,159,170,169,180,191,202)(36,42,48,55,62,70,78,87,96,106,116,127,138,149,160,171,182,181,192,203,211,218)(49,56,63,71,79,88,97,107,117,128,139,150,161,172,183,194,193,204,212,219,224,228)(64,72,80,89,98,108,118,129,140,151,162,173,184,195,190,201,210,217,223,227,230,231)(81,90,99,109,119,130,141,152,163,174,185,196,205,167,178,189,200,209,216,222,226,229)(100,110,120,131,142,153,164,175,186,197,206,213,144,155,166,177,188,199,208,215,221,225)(121,132,143,154,165,176,187,198,207,214,220),(2,4)(6,9)(12,16)(20,25)(30,36)(42,49)(56,64)(72,81)(90,100)(110,121)(122,133)(132,144)(134,145)(146,157)(155,167)(158,169)(170,181)(178,190)(182,193)(194,201)]], +PGAltOnSets(22,2), +PGSymOnSets(22,2), PGAlt, PGSym, ]; @@ -861,8 +861,8 @@ PRIMGRP[253]:=[ [3,6072,1,"2",[[4,1],[6,2],[24,8],[8,1],[12,3]],1,"PSL(2, 23)",["L",[2,23],1],[(1,2,4,8,15,28,50,86,143,118,131)(3,6,12,22,40,70,117,181,93,151,202)(5,10,19,34,45,78,95,154,216,123,188)(7,14,26,47,82,81,135,198,79,132,64)(9,17,31,55,96,156,148,211,37,65,112)(11,21,38,66,98,159,215,207,111,175,100)(13,24,44,76,84,139,115,155,218,247,125)(16,29,52,90,147,209,245,110,173,230,194)(18,33,59,102,164,67,114,178,91,51,88)(20,36,63,109,43,75,126,27,48,69,97)(23,42,73,32,57,99,160,222,249,252,210)(25,46,80,133,197,229,246,237,196,180,191)(30,54,94,152,213,127,192,41,72,121,145)(35,62,107,169,176,221,182,233,77,129,104)(39,68,116,142,205,149,163,225,130,195,183)(49,85,141,204,244,153,214,232,242,241,167)(53,92,150,212,179,140,203,243,253,61,105)(56,58,101,162,224,250,226,71,119,184,234)(60,103,165,158,220,122,187,217,128,193,201)(74,124,190,239,227,172,138,161,223,108,171)(83,137,200,236,157,219,170,89,146,189,134)(87,144,208,238,251,106,168,206,240,166,228)(113,177,231,120,185,235,248,186,199,136,174),(1,3,7)(2,5,11)(4,9,18)(6,13,25)(8,16,30)(10,20,37)(12,23,43)(14,27,49)(17,32,58)(19,35,26)(21,39,69)(22,41,59)(24,45,79)(28,51,89)(29,53,93)(31,56,98)(33,60,104)(34,61,106)(36,64,111)(38,67,115)(40,71,120)(42,74,125)(44,77,130)(46,81,99)(47,83,138)(48,84,140)(50,87,133)(52,91,149)(54,95,155)(55,97,158)(57,100,161)(62,108,144)(63,110,174)(65,66,113)(68,114,179)(70,118,183)(72,122,160)(73,123,189)(75,127,126)(76,128,194)(78,131,196)(80,134,175)(82,136,199)(85,142,206)(86,132,173)(88,145,92)(90,148,192)(94,153,215)(96,157,102)(101,163,162)(103,166,212)(105,167,169)(107,170,229)(109,172,187)(112,176,228)(116,180,231)(117,182,193)(119,129,152)(121,186,237)(124,191,240)(135,171,211)(137,201,234)(139,202,242)(141,185,236)(143,207,220)(146,181,225)(147,210,168)(150,154,217)(151,197,241)(159,221,245)(164,226,214)(165,227,250)(177,232,190)(178,188,238)(184,209,204)(195,235,252)(198,205,213)(203,218,248)(208,219,224)(216,246,223)(222,244,253)(230,251,247)(233,249,243)]], [4,10200960,1,"2",[[210,1],[42,1]],1,"M(23)",["Spor","M(23)",1],[(1,2)(3,5)(4,7)(6,10)(8,13)(9,15)(12,18)(14,20)(16,22)(17,24)(23,30)(25,32)(26,34)(28,36)(29,38)(31,41)(33,44)(37,49)(40,52)(43,55)(45,58)(46,59)(47,60)(48,61)(50,63)(51,65)(53,67)(54,69)(56,71)(57,73)(62,78)(64,81)(66,84)(68,86)(70,89)(74,93)(75,94)(76,96)(77,97)(79,100)(80,102)(82,95)(83,105)(87,108)(88,109)(90,111)(91,113)(92,115)(98,120)(99,122)(101,125)(103,127)(104,129)(106,131)(107,132)(110,136)(112,139)(114,140)(116,143)(117,145)(118,146)(119,148)(121,151)(123,153)(124,154)(126,157)(128,160)(130,161)(133,164)(134,166)(137,142)(138,168)(141,152)(144,173)(147,170)(149,178)(150,180)(156,186)(158,187)(162,182)(163,190)(165,193)(167,188)(171,196)(172,197)(174,195)(175,199)(176,201)(177,189)(179,204)(181,206)(183,184)(191,211)(192,207)(194,214)(198,217)(202,213)(205,224)(208,225)(215,230)(216,231)(219,234)(220,235)(222,236)(223,233)(228,238)(232,243)(239,241)(240,248)(244,251)(245,249)(247,252),(1,3,6,11)(2,4,8,14)(5,9,16,23)(7,12,19,26)(10,17)(15,21,28,37)(18,25,33,45)(20,27,35,47)(22,29,39,51)(24,31,42,54)(30,40,44,57)(32,43,56,72)(34,46,36,48)(38,50,64,82)(41,53,68,87)(49,62,79,101)(52,66,73,92)(55,70,90,112)(58,74,67,85)(59,75,95,89)(60,76)(61,77,98,121)(63,80,103,128)(65,83,81,104)(69,88,110,137)(71,91,114,141)(78,99,123,113)(84,106)(86,107,133,165)(93,116,144,174)(94,117)(96,118,147,132)(97,119,149,179)(100,124,155,185)(102,126,158,188)(105,130,162,189)(108,134,140,170)(109,135,167,194)(111,138,169,136)(115,142,171,161)(120,150,127,159)(122,152,182,129)(125,156,143,172)(131,163,191,212)(145,175,200,220)(146,176,202,222)(148,177,203,157)(151,181)(153,183,207,190)(154,184,208,226)(164,192,168,195)(173,198,218,233)(180,205)(186,209,224,206)(187,210)(193,213,228,240)(196,215)(197,216)(199,219,201,221)(204,223,237,235)(211,227,239,247)(214,229,234,244)(217,232,236,245)(225,238,246,248)(230,241)(231,242,249,253)(243,250)(251,252)]], [5,10200960,1,"2",[[112,1],[140,1]],1,"M(23)",["Spor","M(23)",1],[(1,2)(3,5)(4,7)(6,10)(8,13)(9,15)(11,18)(12,19)(14,22)(16,24)(17,26)(20,30)(21,32)(23,35)(25,38)(27,40)(29,42)(31,44)(33,46)(34,48)(36,51)(37,53)(39,56)(41,58)(43,60)(45,63)(47,65)(49,67)(50,69)(54,73)(57,77)(59,80)(61,82)(64,86)(66,89)(68,92)(70,94)(72,96)(74,99)(75,100)(76,101)(78,87)(79,105)(83,109)(84,110)(85,112)(88,116)(90,117)(93,106)(95,123)(97,125)(98,126)(102,114)(103,130)(104,132)(107,135)(111,139)(113,141)(115,143)(118,145)(119,136)(120,147)(121,149)(122,137)(127,155)(128,156)(129,158)(131,160)(134,162)(138,167)(140,168)(142,170)(146,174)(148,176)(150,178)(152,180)(153,177)(154,181)(157,185)(161,190)(163,191)(164,192)(165,193)(169,195)(171,199)(172,201)(179,205)(182,200)(183,208)(184,210)(186,212)(187,213)(188,215)(196,203)(198,214)(202,220)(204,216)(211,226)(217,230)(218,231)(219,232)(222,225)(224,235)(227,233)(228,238)(236,241)(240,244)(242,246)(243,248)(245,249)(247,251)(250,252),(1,3,6,11)(2,4,8,14)(5,9,16,25)(7,12,20,31)(10,17,27,41)(13,21,33,47)(15,23,36,52)(18,28,32,45)(19,29)(22,34,49,68)(24,37,54,74)(26,39,51,71)(30,43,61,83)(35,50,70,95)(38,55,75,60)(40,57,78,104)(42,59,81,107)(44,62,84,111)(46,64,87,115)(48,66,90,118)(53,72,97,116)(56,76,102,129)(58,79,100,89)(63,85,113,142)(65,88,73,98)(67,91,119,146)(69,93,121,150)(77,103,131,161)(80,106,134,163)(82,108,136,165)(86,114,96,124)(92,120,148,177)(94,122,151,179)(99,127)(101,128,157,186)(105,133,145,173)(109,137,166,194)(110,138)(112,140,169,197)(117,144,172,202)(123,152,135,164)(125,153)(126,154,182,207)(130,159,188,141)(139,162,174,149)(143,171,200,219)(147,175,203,221)(155,183,209,181)(156,184)(158,187,214,193)(160,189)(167,195,212,178)(168,196)(170,198,191,216)(176,204,222,233)(180,206,224,236)(185,211,227,190)(192,217)(199,218)(201,210,225,237)(205,223,234,208)(213,228,239,243)(215,229,240,245)(226,232,242,247)(231,241)(235,238)(244,248,246,250)(251,253)]], -[6,12926008369442488320000,1,"2",[[210,1],[42,1]],1,"Alt(23)",["A",23,1],[(2,3,5,8,12,17,23,30,38,47,57,68,80,93,107,122,138,155,173,192,212)(4,7,11,16,22,29,37,46,56,67,79,92,106,121,137,154,172,191,211,232,253)(6,10,15,21,28,36,45,55,66,78,91,105,120,136,153,171,190,210,231,252,233)(9,14,20,27,35,44,54,65,77,90,104,119,135,152,170,189,209,230,251,213,234)(13,19,26,34,43,53,64,76,89,103,118,134,151,169,188,208,229,250,193,214,235)(18,25,33,42,52,63,75,88,102,117,133,150,168,187,207,228,249,174,194,215,236)(24,32,41,51,62,74,87,101,116,132,149,167,186,206,227,248,156,175,195,216,237)(31,40,50,61,73,86,100,115,131,148,166,185,205,226,247,139,157,176,196,217,238)(39,49,60,72,85,99,114,130,147,165,184,204,225,246,123,140,158,177,197,218,239)(48,59,71,84,98,113,129,146,164,183,203,224,245,108,124,141,159,178,198,219,240)(58,70,83,97,112,128,145,163,182,202,223,244,94,109,125,142,160,179,199,220,241)(69,82,96,111,127,144,162,181,201,222,243,81,95,110,126,143,161,180,200,221,242),(1,2,4)(3,6,7)(5,9,11)(8,13,16)(12,18,22)(17,24,29)(23,31,37)(30,39,46)(38,48,56)(47,58,67)(57,69,79)(68,81,92)(80,94,106)(93,108,121)(107,123,137)(122,139,154)(138,156,172)(155,174,191)(173,193,211)(192,213,232)(212,233,253)]], -[7,25852016738884976640000,0,"2",[[210,1],[42,1]],1,"Sym(23)",["A",23,1],[(1,2,3,5,7,10,13,17,21,26,31,37,43,50,57,65,73,82,91,101,111,122,133)(4,6,8,11,14,18,22,27,32,38,44,51,58,66,74,83,92,102,112,123,134,146,145)(9,12,15,19,23,28,33,39,45,52,59,67,75,84,93,103,113,124,135,147,158,157,169)(16,20,24,29,34,40,46,53,60,68,76,85,94,104,114,125,136,148,159,171,170,181,193)(25,30,35,41,47,54,61,69,77,86,95,105,115,126,137,149,160,172,183,182,194,205,217)(36,42,48,55,62,70,78,87,96,106,116,127,138,150,161,173,184,196,195,206,218,227,235)(49,56,63,71,79,88,97,107,117,128,139,151,162,174,185,197,208,207,219,228,236,242,247)(64,72,80,89,98,108,118,129,140,152,163,175,186,198,209,216,220,229,237,243,248,251,253)(81,90,99,109,119,130,141,153,164,176,187,199,210,221,192,204,215,226,234,241,246,250,252)(100,110,120,131,142,154,165,177,188,200,211,222,230,168,180,191,203,214,225,233,240,245,249)(121,132,143,155,166,178,189,201,212,223,231,238,144,156,167,179,190,202,213,224,232,239,244),(2,4)(6,9)(12,16)(20,25)(30,36)(42,49)(56,64)(72,81)(90,100)(110,121)(132,144)(133,145)(146,157)(156,168)(158,170)(171,182)(180,192)(183,195)(196,207)(204,216)(208,220)]], +PGAltOnSets(23,2), +PGSymOnSets(23,2), PGAlt, PGSym, ]; @@ -1259,8 +1259,8 @@ PRIMGRP[276]:=[ [2,12144,0,"2",[[22,10],[44,1],[11,1]],1,"PGL(2, 23)",["L",[2,23],1],[(1,2,4,8,15,28,49,83,132,190,232,269,275,173,143,134,135,194,207,252,179,224)(3,6,12,22,41,70,113,168,205,229,48,82,131,188,244,272,276,262,95,147,210,256)(5,10,19,35,59,100,154,181,62,105,123,178,211,257,242,259,193,209,255,7,14,26)(9,17,32,54,92,71,115,53,90,141,202,139,76,124,180,239,128,183,240,60,69,114)(11,21,39,66,110,165,222,265,273,254,18,34,58,98,44,75,122,177,117,104,157,213)(13,24,43,73,118,172,40,68,112,166,156)(16,30,46,79,127,25,45,77,23,42,36,61,103,109,163,169,225,184,243,93,144,206)(20,37,63,106,159,216,246,164,221,264,29,51,87,137,198,149,212,227,223,267,189,236)(27,47,81,130,187,101,155,214,186,182,111,152,175,233,260,215,167,31,33,56,96,148)(38,65,108,160,218,217,261,268,199,249,64,107,161,88,138,200,250,52,89,140,201,245)(50,85,72,116,170,226,241,270,57,97,150,55,94,146,151,203,74,120,174,231,247,158)(67,91,142,204,253,197,248,266,274,145,208,78,125,121,176,235,84,133,192,230,234,263)(80,129,185,86,136,196,119,102,99,153,191,171,228,195,237,271,238,126,162,219,251,220),(1,3,7)(2,5,11)(4,9,18)(6,13,25)(8,16,31)(10,20,38)(12,23,34)(14,27,48)(15,29,52)(17,33,57)(19,36,62)(21,40,69)(22,41,71)(24,44,76)(26,46,80)(28,50,86)(30,53,91)(32,55,95)(35,60,102)(37,64,47)(39,67,111)(42,72,117)(43,74,121)(45,78,126)(49,84,134)(51,88,139)(54,93,145)(56,92,143)(58,99,66)(59,101,156)(61,104,158)(63,89,77)(65,109,164)(68,113,169)(70,110,103)(73,119,173)(75,123,179)(79,128,184)(81,83,115)(82,94,90)(85,135,195)(87,138,114)(96,149,108)(97,151,100)(98,152,208)(105,106,160)(107,162,216)(112,167,154)(116,171,229)(118,132,191)(120,175,234)(122,146,209)(124,181,153)(125,182,241)(127,174,232)(129,186,188)(130,141,203)(131,189,245)(133,193,235)(136,197,228)(137,199,231)(140,176,236)(142,205,190)(144,207,187)(147,148,211)(150,213,259)(155,177,237)(157,215,185)(159,217,262)(161,170,227)(163,220,263)(165,202,252)(166,223,268)(168,224,257)(172,230,270)(178,238,243)(180,240,219)(183,242,248)(192,246,218)(194,221,200)(196,247,210)(198,201,251)(204,254,272)(206,214,260)(212,258,249)(222,266,244)(225,269,226)(233,271,276)(239,253,255)(250,273,267)(256,274,275)(261,265,264)]], 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+PGAltOnSets(24,2), +PGSymOnSets(24,2), PGAlt, PGSym, ]; @@ -1366,8 +1366,8 @@ PGAlt, PGSym, ]; PRIMGRP[286]:=[ 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+PGAltOnSets(13,3), +PGSymOnSets(13,3), PGAlt, PGSym, ]; @@ -1541,8 +1541,8 @@ PRIMGRP[300]:=[ [5,31200,0,"2",[[13,1],[26,3],[52,4]],1,"PSL(2, 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+PGAltOnSets(25,2), +PGSymOnSets(25,2), PGAlt, PGSym, ]; diff --git a/data/gps20.g b/data/gps20.g index 10c14be..cabd3dd 100644 --- a/data/gps20.g +++ b/data/gps20.g @@ -180,8 +180,8 @@ PRIMGRP[2080]:=[ [13,51615733565620224000,1,"2",[[1023,1],[1056,1]],1,"POmega-(12, 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+PGAltOnSets(65,2), +PGSymOnSets(65,2), PGAlt, PGSym, ]; @@ -671,8 +671,8 @@ PGAlt, PGSym, ]; PRIMGRP[2145]:=[ 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+PGAltOnSets(66,2), +PGSymOnSets(66,2), PGAlt, PGSym, ]; diff --git a/data/gps21.g b/data/gps21.g index 219d64a..6491f35 100644 --- a/data/gps21.g +++ b/data/gps21.g @@ -660,8 +660,8 @@ PGSym, PRIMGRP[2211]:=[ [1,150348,1,"2",[[68,16],[17,2],[34,32]],1,"PSL(2, 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+PGAltOnSets(67,2), +PGSymOnSets(67,2), PGAlt, PGSym, ]; diff --git a/data/gps22.g b/data/gps22.g index dc719da..3620e7c 100644 --- a/data/gps22.g +++ b/data/gps22.g @@ -326,8 +326,8 @@ PGSym, PRIMGRP[2278]:=[ [1,150348,1,"2",[[66,18],[33,33]],1,"PSL(2, 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+PGAltOnSets(68,2), +PGSymOnSets(68,2), PGAlt, PGSym, ]; @@ -499,8 +499,8 @@ PGSym, ]; PRIMGRP[2300]:=[ 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+PGAltOnSets(25,3), +PGSymOnSets(25,3), PGAlt, PGSym, ]; @@ -799,8 +799,8 @@ PGAlt, PGSym, ]; PRIMGRP[2346]:=[ 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+PGAltOnSets(69,2), +PGSymOnSets(69,2), PGAlt, PGSym, ]; @@ -1039,8 +1039,8 @@ PRIMGRP[2380]:=[ [2,68518981440,1,"2",[[182,1],[2197,1]],1,"PSp(4, 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PGPgl(4,13), diff --git a/data/gps24.g b/data/gps24.g index b2b851d..b0c0534 100644 --- a/data/gps24.g +++ b/data/gps24.g @@ -57,8 +57,8 @@ PGAlt, PGSym, ]; PRIMGRP[2415]:=[ 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+PGAltOnSets(70,2), +PGSymOnSets(70,2), PGAlt, PGSym, ]; @@ -474,8 +474,8 @@ PGSym, PRIMGRP[2485]:=[ [1,178920,1,"2",[[18,2],[72,17],[36,34]],1,"PSL(2, 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+PGAltOnSets(71,2), +PGSymOnSets(71,2), PGAlt, PGSym, ]; diff --git a/data/gps25.g b/data/gps25.g index 8b08e71..7fe6477 100644 --- a/data/gps25.g +++ b/data/gps25.g @@ -422,8 +422,8 @@ PGSym, PRIMGRP[2556]:=[ 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+PGAltOnSets(72,2), +PGSymOnSets(72,2), PGAlt, PGSym, ]; @@ -678,8 +678,8 @@ PGAlt, PGSym, ]; PRIMGRP[2600]:=[ 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+PGAltOnSets(26,3), +PGSymOnSets(26,3), PGAlt, PGSym, ]; diff --git a/data/gps26.g b/data/gps26.g index 4585ff9..dd9d566 100644 --- a/data/gps26.g +++ b/data/gps26.g @@ -125,8 +125,8 @@ PGSym, PRIMGRP[2628]:=[ 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+PGAltOnSets(73,2), +PGSymOnSets(73,2), PGAlt, PGSym, ]; @@ -608,8 +608,8 @@ PGSym, PRIMGRP[2701]:=[ 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+PGAltOnSets(74,2), +PGSymOnSets(74,2), PGAlt, PGSym, ]; diff --git a/data/gps27.g b/data/gps27.g index 2962ddb..580db7c 100644 --- a/data/gps27.g +++ b/data/gps27.g @@ -395,8 +395,8 @@ PGAlt, PGSym, ]; PRIMGRP[2775]:=[ 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+PGAltOnSets(75,2), +PGSymOnSets(75,2), PGAlt, PGSym, ]; diff --git a/data/gps28.g b/data/gps28.g index e1d1064..c8d0e6d 100644 --- a/data/gps28.g +++ b/data/gps28.g @@ -227,8 +227,8 @@ PRIMGRP[2850]:=[ 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+PGAltOnSets(76,2), +PGSymOnSets(76,2), PGAlt, PGSym, ]; @@ -699,15 +699,15 @@ PGSym, PRIMGRP[2925]:=[ 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+PGAltOnSets(27,3), +PGSymOnSets(27,3), PGAlt, PGSym, ]; PRIMGRP[2926]:=[ 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+PGAltOnSets(77,2), +PGSymOnSets(77,2), PGAlt, PGSym, ]; diff --git a/data/gps29.g b/data/gps29.g index 98aa723..ce1c0c0 100644 --- a/data/gps29.g +++ b/data/gps29.g @@ -438,12 +438,12 @@ PGAlt, PGSym, ]; PRIMGRP[3003]:=[ 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+PGAltOnSets(14,6), +PGSymOnSets(14,6), +PGAltOnSets(15,5), +PGSymOnSets(15,5), +PGAltOnSets(78,2), +PGSymOnSets(78,2), PGAlt, PGSym, ]; diff --git a/data/gps3.g b/data/gps3.g index b7fc095..2792161 100644 --- a/data/gps3.g +++ b/data/gps3.g @@ -167,8 +167,8 @@ PRIMGRP[325]:=[ [8,15600,0,"2",[[6,2],[24,4],[12,6],[48,3]],1,"PSL(2, 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+PGAltOnSets(26,2), +PGSymOnSets(26,2), PGAlt, PGSym, ]; @@ -191,8 +191,8 @@ PGSym, PRIMGRP[330]:=[ 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+PGAltOnSets(11,4), +PGSymOnSets(11,4), PGAlt, PGSym, ]; @@ -447,8 +447,8 @@ PRIMGRP[351]:=[ [5,4585351680,1,"2",[[224,1],[126,1]],1,"O(7, 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+PGAltOnSets(27,2), +PGSymOnSets(27,2), PGAlt, PGSym, ]; @@ -642,8 +642,8 @@ PRIMGRP[364]:=[ [3,4585351680,1,"2",[[243,1],[120,1]],1,"O(7, 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+PGAltOnSets(28,2), +PGSymOnSets(28,2), PGAlt, PGSym, ]; @@ -939,8 +939,8 @@ PGSym, PRIMGRP[406]:=[ [1,12180,1,"2",[[30,7],[15,13]],1,"PSL(2, 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+PGAltOnSets(29,2), +PGSymOnSets(29,2), PGAlt, PGSym, ]; @@ -1151,8 +1151,8 @@ PGSym, PRIMGRP[435]:=[ [1,12180,1,"2",[[7,2],[14,12],[28,9]],1,"PSL(2, 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+PGAltOnSets(30,2), +PGSymOnSets(30,2), PGAlt, PGSym, ]; diff --git a/data/gps30.g b/data/gps30.g index 66c8ab2..e3d0b97 100644 --- a/data/gps30.g +++ b/data/gps30.g @@ -41,8 +41,8 @@ PGAlt, PGSym, ]; PRIMGRP[3060]:=[ 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+PGAltOnSets(18,4), +PGSymOnSets(18,4), PGAlt, PGSym, ]; @@ -207,8 +207,8 @@ PGSym, PRIMGRP[3081]:=[ 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+PGAltOnSets(79,2), +PGSymOnSets(79,2), PGAlt, PGSym, ]; diff --git a/data/gps31.g b/data/gps31.g index 2cdef47..b39480b 100644 --- a/data/gps31.g +++ b/data/gps31.g @@ -119,8 +119,8 @@ PGSym, PRIMGRP[3160]:=[ 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+PGAltOnSets(80,2), +PGSymOnSets(80,2), PGAlt, PGSym, ]; @@ -658,8 +658,8 @@ PRIMGRP[3240]:=[ 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175,3188,3200,3210,3219,3226,3232,3236,3239)(784,812,840,869,898,928,958,989,1020,1052,1084,1117,1150,1184,1218,1253,1288,1324,1360,1397,1434,1472,1510,1549,1588,1628,1668,1709,1749,1790,1830,1871,1911,1952,1992,2033,2073,2114,2154,2195,2235,2276,2316,2357,2397,2438,2478,2519,2559,2600,2640,2681,2721,2665,2706,2746,2784,2820,2855,2888,2920,2950,2979,3006,3032,3056,3079,3100,3120,3138,3155,3170,3184,3196,3207,3216,3224,3230,3235,3238,3240)(841,870,899,929,959,990,1021,1053,1085,1118,1151,1185,1219,1254,1289,1325,1361,1398,1435,1473,1511,1550,1589,1629,1669,1710,1750,1791,1831,1872,1912,1953,1993,2034,2074,2115,2155,2196,2236,2277,2317,2358,2398,2439,2479,2520,2560,2601,2641,2682,2722,2760,2583,2624,2664,2705,2745,2783,2819,2854,2887,2919,2949,2978,3005,3031,3055,3078,3099,3119,3137,3154,3169,3183,3195,3206,3215,3223,3229,3234,3237)(900,930,960,991,1022,1054,1086,1119,1152,1186,1220,1255,1290,1326,1362,1399,1436,1474,1512,1551,1590,1630,1670,1711,1751,1792,1832,1873,1913,1954,1994,2035,2075,2116,2156,2197,2237,2278,2318,2359,2399,2440,2480,2521,2561,2602,2642,2683,2723,2761,2797,2501,2542,2582,2623,2663,2704,2744,2782,2818,2853,2886,2918,2948,2977,3004,3030,3054,3077,3098,3118,3136,3153,3168,3182,3194,3205,3214,3222,3228,3233)(961,992,1023,1055,1087,1120,1153,1187,1221,1256,1291,1327,1363,1400,1437,1475,1513,1552,1591,1631,1671,1712,1752,1793,1833,1874,1914,1955,1995,2036,2076,2117,2157,2198,2238,2279,2319,2360,2400,2441,2481,2522,2562,2603,2643,2684,2724,2762,2798,2833,2419,2460,2500,2541,2581,2622,2662,2703,2743,2781,2817,2852,2885,2917,2947,2976,3003,3029,3053,3076,3097,3117,3135,3152,3167,3181,3193,3204,3213,3221,3227)(1024,1056,1088,1121,1154,1188,1222,1257,1292,1328,1364,1401,1438,1476,1514,1553,1592,1632,1672,1713,1753,1794,1834,1875,1915,1956,1996,2037,2077,2118,2158,2199,2239,2280,2320,2361,2401,2442,2482,2523,2563,2604,2644,2685,2725,2763,2799,2834,2867,2337,2378,2418,2459,2499,2540,2580,2621,2661,2702,2742,2780,2816,2851,2884,2916,2946,2975,3002,3028,3052,3075,3096,3116,3134,3151,3166,3180,3192,3203,3212,3220)(1089,1122,1155,1189,1223,1258,1293,1329,1365,1402,1439,1477,1515,1554,1593,1633,1673,1714,1754,1795,1835,1876,1916,1957,1997,2038,2078,2119,2159,2200,2240,2281,2321,2362,2402,2443,2483,2524,2564,2605,2645,2686,2726,2764,2800,2835,2868,2900,2255,2296,2336,2377,2417,2458,2498,2539,2579,2620,2660,2701,2741,2779,2815,2850,2883,2915,2945,2974,3001,3027,3051,3074,3095,3115,3133,3150,3165,3179,3191,3202,3211)(1156,1190,1224,1259,1294,1330,1366,1403,1440,1478,1516,1555,1594,1634,1674,1715,1755,1796,1836,1877,1917,1958,1998,2039,2079,2120,2160,2201,2241,2282,2322,2363,2403,2444,2484,2525,2565,2606,2646,2687,2727,2765,2801,2836,2869,2901,2931,2173,2214,2254,2295,2335,2376,2416,2457,2497,2538,2578,2619,2659,2700,2740,2778,2814,2849,2882,2914,2944,2973,3000,3026,3050,3073,3094,3114,3132,3149,3164,3178,3190,3201)(1225,1260,1295,1331,1367,1404,1441,1479,1517,1556,1595,1635,1675,1716,1756,1797,1837,1878,1918,1959,1999,2040,2080,2121,2161,2202,2242,2283,2323,2364,2404,2445,2485,2526,2566,2607,2647,2688,2728,2766,2802,2837,2870,2902,2932,2961,2091,2132,2172,2213,2253,2294,2334,2375,2415,2456,2496,2537,2577,2618,2658,2699,2739,2777,2813,2848,2881,2913,2943,2972,2999,3025,3049,3072,3093,3113,3131,3148,3163,3177,3189)(1296,1332,1368,1405,1442,1480,1518,1557,1596,1636,1676,1717,1757,1798,1838,1879,1919,1960,2000,2041,2081,2122,2162,2203,2243,2284,2324,2365,2405,2446,2486,2527,2567,2608,2648,2689,2729,2767,2803,2838,2871,2903,2933,2962,2989,2009,2050,2090,2131,2171,2212,2252,2293,2333,2374,2414,2455,2495,2536,2576,2617,2657,2698,2738,2776,2812,2847,2880,2912,2942,2971,2998,3024,3048,3071,3092,3112,3130,3147,3162,3176)(1369,1406,1443,1481,1519,1558,1597,1637,1677,1718,1758,1799,1839,1880,1920,1961,2001,2042,2082,2123,2163,2204,2244,2285,2325,2366,2406,2447,2487,2528,2568,2609,2649,2690,2730,2768,2804,2839,2872,2904,2934,2963,2990,3016,1927,1968,2008,2049,2089,2130,2170,2211,2251,2292,2332,2373,2413,2454,2494,2535,2575,2616,2656,2697,2737,2775,2811,2846,2879,2911,2941,2970,2997,3023,3047,3070,3091,3111,3129,3146,3161)(1444,1482,1520,1559,1598,1638,1678,1719,1759,1800,1840,1881,1921,1962,2002,2043,2083,2124,2164,2205,2245,2286,2326,2367,2407,2448,2488,2529,2569,2610,2650,2691,2731,2769,2805,2840,2873,2905,2935,2964,2991,3017,3041,1845,1886,1926,1967,2007,2048,2088,2129,2169,2210,2250,2291,2331,2372,2412,2453,2493,2534,2574,2615,2655,2696,2736,2774,2810,2845,2878,2910,2940,2969,2996,3022,3046,3069,3090,3110,3128,3145)(1521,1560,1599,1639,1679,1720,1760,1801,1841,1882,1922,1963,2003,2044,2084,2125,2165,2206,2246,2287,2327,2368,2408,2449,2489,2530,2570,2611,2651,2692,2732,2770,2806,2841,2874,2906,2936,2965,2992,3018,3042,3065,1763,1804,1844,1885,1925,1966,2006,2047,2087,2128,2168,2209,2249,2290,2330,2371,2411,2452,2492,2533,2573,2614,2654,2695,2735,2773,2809,2844,2877,2909,2939,2968,2995,3021,3045,3068,3089,3109,3127)(1600,1640,1680,1721,1761,1802,1842,1883,1923,1964,2004,2045,2085,2126,2166,2207,2247,2288,2328,2369,240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+PGAltOnSets(81,2), +PGSymOnSets(81,2), PGAlt, PGSym, ]; diff --git a/data/gps32.g b/data/gps32.g index aa27a27..dd05d9d 100644 --- a/data/gps32.g +++ b/data/gps32.g @@ -169,8 +169,8 @@ PRIMGRP[3276]:=[ 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+PGAltOnSets(28,3), +PGSymOnSets(28,3), PGAlt, PGSym, ]; @@ -490,8 +490,8 @@ PRIMGRP[3321]:=[ 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+PGAltOnSets(82,2), +PGSymOnSets(82,2), PGAlt, PGSym, ]; diff --git a/data/gps33.g b/data/gps33.g index c6ee4ad..d727e68 100644 --- a/data/gps33.g +++ b/data/gps33.g @@ -339,8 +339,8 @@ PGSym, PRIMGRP[3403]:=[ 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+PGAltOnSets(83,2), +PGSymOnSets(83,2), PGAlt, PGSym, ]; diff --git a/data/gps34.g b/data/gps34.g index 1733f06..8febecc 100644 --- a/data/gps34.g +++ b/data/gps34.g @@ -204,8 +204,8 @@ PGSym, PRIMGRP[3486]:=[ 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+PGAltOnSets(84,2), +PGSymOnSets(84,2), PGAlt, PGSym, ]; diff --git a/data/gps35.g b/data/gps35.g index db0e23e..84a13ae 100644 --- a/data/gps35.g +++ b/data/gps35.g @@ -59,8 +59,8 @@ PGAlt, PGSym, ]; PRIMGRP[3570]:=[ 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+PGAltOnSets(85,2), +PGSymOnSets(85,2), PGAlt, PGSym, ]; @@ -631,14 +631,14 @@ PGAlt, PGSym, ]; PRIMGRP[3654]:=[ 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+PGAltOnSets(29,3), +PGSymOnSets(29,3), PGAlt, PGSym, ]; PRIMGRP[3655]:=[ 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+PGAltOnSets(86,2), +PGSymOnSets(86,2), PGAlt, PGSym, ]; diff --git a/data/gps37.g b/data/gps37.g index 2bd0c65..c460baa 100644 --- a/data/gps37.g +++ b/data/gps37.g @@ -125,8 +125,8 @@ PGAlt, PGSym, ]; PRIMGRP[3741]:=[ 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+PGAltOnSets(87,2), +PGSymOnSets(87,2), PGAlt, PGSym, ]; @@ -616,8 +616,8 @@ PGAlt, PGSym, ]; PRIMGRP[3828]:=[ 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+PGAltOnSets(88,2), +PGSymOnSets(88,2), PGAlt, PGSym, ]; diff --git a/data/gps38.g b/data/gps38.g index f3551fd..ccb81c1 100644 --- a/data/gps38.g +++ b/data/gps38.g @@ -125,8 +125,8 @@ PGAlt, PGSym, ]; PRIMGRP[3876]:=[ 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+PGAltOnSets(19,4), +PGSymOnSets(19,4), PGAlt, PGSym, ]; @@ -419,8 +419,8 @@ PGSym, PRIMGRP[3916]:=[ 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+PGAltOnSets(89,2), +PGSymOnSets(89,2), PGAlt, PGSym, ]; diff --git a/data/gps39.g b/data/gps39.g index 6d5415e..0cde976 100644 --- a/data/gps39.g +++ b/data/gps39.g @@ -195,8 +195,8 @@ PGSym, PRIMGRP[4005]:=[ 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99)(3268,3313)(3314,3359)(3344,3360)]], +PGAltOnSets(90,2), +PGSymOnSets(90,2), PGAlt, PGSym, ]; @@ -576,8 +576,8 @@ PGSym, ]; PRIMGRP[4060]:=[ 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+PGAltOnSets(30,3), +PGSymOnSets(30,3), PGAlt, PGSym, ]; @@ -780,8 +780,8 @@ PGSym, PRIMGRP[4095]:=[ 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+PGAltOnSets(91,2), +PGSymOnSets(91,2), PGAlt, PGSym, ]; diff --git a/data/gps4.g b/data/gps4.g index 328885f..b5a10a8 100644 --- a/data/gps4.g +++ b/data/gps4.g @@ -15,8 +15,8 @@ PGAlt, PGSym, ]; PRIMGRP[455]:=[ 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+PGAltOnSets(15,3), +PGSymOnSets(15,3), PGAlt, PGSym, ]; @@ -79,8 +79,8 @@ PGSym, PRIMGRP[462]:=[ 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+PGAltOnSets(11,5), +PGSymOnSets(11,5), PGPsl(2,461), PGPgl(2,461), PGAlt, @@ -116,8 +116,8 @@ PRIMGRP[465]:=[ [1,14880,1,"2",[[32,7],[8,2],[16,14]],1,"PSL(2, 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+PGAltOnSets(31,2), +PGSymOnSets(31,2), PGAlt, PGSym, ]; @@ -292,8 +292,8 @@ PRIMGRP[495]:=[ 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+PGAltOnSets(12,4), +PGSymOnSets(12,4), PGAlt, PGSym, ]; @@ -306,8 +306,8 @@ PRIMGRP[496]:=[ [6,32736,1,"2",[[33,15]],1,"PSL(2, 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+PGAltOnSets(32,2), +PGSymOnSets(32,2), PGAlt, PGSym, ]; @@ -586,8 +586,8 @@ PRIMGRP[528]:=[ [3,24815256521932800,1,"2",[[527,1]],2,"PSp(10, 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+PGAltOnSets(33,2), +PGSymOnSets(33,2), PGAlt, PGSym, ]; @@ -847,14 +847,14 @@ PGSym, PRIMGRP[560]:=[ 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+PGAltOnSets(16,3), +PGSymOnSets(16,3), PGAlt, PGSym, ]; PRIMGRP[561]:=[ 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-[2,295232799039604140847618609643520000000,0,"2",[[496,1],[64,1]],1,"Sym(34)",["A",34,1],[(1,2,3,5,7,10,13,17,21,26,31,37,43,50,57,65,73,82,91,101,111,122,133,145,157,170,183,197,211,226,241,257,273,290)(4,6,8,11,14,18,22,27,32,38,44,51,58,66,74,83,92,102,112,123,134,146,158,171,184,198,212,227,242,258,274,291,308,307)(9,12,15,19,23,28,33,39,45,52,59,67,75,84,93,103,113,124,135,147,159,172,185,199,213,228,243,259,275,292,309,326,325,342)(16,20,24,29,34,40,46,53,60,68,76,85,94,104,114,125,136,148,160,173,186,200,214,229,244,260,276,293,310,327,344,343,360,377)(25,30,35,41,47,54,61,69,77,86,95,105,115,126,137,149,161,174,187,201,215,230,245,261,277,294,311,328,345,362,361,378,395,412)(36,42,48,55,62,70,78,87,96,106,116,127,138,150,162,175,188,202,216,231,246,262,278,295,312,329,346,363,380,379,396,413,430,447)(49,56,63,71,79,88,97,107,117,128,139,151,163,176,189,203,217,232,247,263,279,296,313,330,347,364,381,398,397,414,431,448,465,482)(64,72,80,89,98,108,118,129,140,152,164,177,190,204,218,233,248,264,280,297,314,331,348,365,382,399,416,415,432,449,466,483,497,510)(81,90,99,109,119,130,141,153,165,178,191,205,219,234,249,265,281,298,315,332,349,366,383,400,417,434,433,450,467,484,498,511,522,532)(100,110,120,131,142,154,166,179,192,206,220,235,250,266,282,299,316,333,350,367,384,401,418,435,452,451,468,485,499,512,523,533,541,548)(121,132,143,155,167,180,193,207,221,236,251,267,283,300,317,334,351,368,385,402,419,436,453,470,469,486,500,513,524,534,542,549,554,558)(144,156,168,181,194,208,222,237,252,268,284,301,318,335,352,369,386,403,420,437,454,471,464,481,496,509,521,531,540,547,553,557,560,561)(169,182,195,209,223,238,253,269,285,302,319,336,353,370,387,404,421,438,455,472,487,429,446,463,480,495,508,520,530,539,546,552,556,559)(196,210,224,239,254,270,286,303,320,337,354,371,388,405,422,439,456,473,488,501,394,411,428,445,462,479,494,507,519,529,538,545,551,555)(225,240,255,271,287,304,321,338,355,372,389,406,423,440,457,474,489,502,514,359,376,393,410,427,444,461,478,493,506,518,528,537,544,550)(256,272,288,305,322,339,356,373,390,407,424,441,458,475,490,503,515,525,324,341,358,375,392,409,426,443,460,477,492,505,517,527,536,543)(289,306,323,340,357,374,391,408,425,442,459,476,491,504,516,526,535),(2,4)(6,9)(12,16)(20,25)(30,36)(42,49)(56,64)(72,81)(90,100)(110,121)(132,144)(156,169)(182,196)(210,225)(240,256)(272,289)(290,307)(306,324)(308,325)(326,343)(341,359)(344,361)(362,379)(376,394)(380,397)(398,415)(411,429)(416,433)(434,451)(446,464)(452,469)(470,481)]], +PGAltOnSets(34,2), +PGSymOnSets(34,2), PGAlt, PGSym, ]; @@ -1085,8 +1085,8 @@ PGAlt, PGSym, ]; PRIMGRP[595]:=[ 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+PGAltOnSets(35,2), +PGSymOnSets(35,2), PGAlt, PGSym, ]; diff --git a/data/gps5.g b/data/gps5.g index ab205b7..5cdfb36 100644 --- a/data/gps5.g +++ b/data/gps5.g @@ -906,8 +906,8 @@ PGAlt, PGSym, ]; PRIMGRP[630]:=[ 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+PGAltOnSets(36,2), +PGSymOnSets(36,2), PGAlt, PGSym, ]; diff --git a/data/gps6.g b/data/gps6.g index 3b320f9..18e23ac 100644 --- a/data/gps6.g +++ b/data/gps6.g @@ -117,8 +117,8 @@ PGSym, PRIMGRP[666]:=[ [1,25308,1,"2",[[38,9],[19,17]],1,"PSL(2, 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+PGAltOnSets(37,2), +PGSymOnSets(37,2), PGAlt, PGSym, ]; @@ -248,8 +248,8 @@ PGAlt, PGSym, ]; PRIMGRP[680]:=[ 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+PGAltOnSets(17,3), +PGSymOnSets(17,3), PGAlt, PGSym, ]; @@ -396,8 +396,8 @@ PGSym, PRIMGRP[703]:=[ [1,25308,1,"2",[[36,11],[9,2],[18,16]],1,"PSL(2, 37)",["L",[2,37],1],[(1,124,332,19,4,74,15,25,334)(2,634,323,524,134,573,694,621,550)(3,118,117,98,75,125,14,73,24)(6,662,590,457,247,11,449,563,60)(7,131,612,256,692,265,485,566,196)(8,122,30,388,688,444,468,376,217)(9,181,328,39,411,262,622,52,589)(10,564,582,552,500,537,384,561,87)(12,696,59,644,370,605,576,345,682)(13,598,31,338,526,183,413,513,586)(16,331,351,120,330,121,83,99,72)(17,693,463,689,649,348,701,691,469)(18,618,428,581,188,532,471,258,359)(20,82,103,23,78,337,100,81,352)(21,316,102,358,169,61,558,208,254)(22,551,448,515,648,53,496,218,366)(26,647,639,170,51,245,114,193,165)(27,88,458,570,84,173,506,80,546)(28,476,698,409,48,482,144,174,308)(29,159,235,261,319,343,168,152,171)(32,309,540,50,484,259,209,403,478)(33,505,439,514,279,486,502,619,517)(34,141,422,609,391,222,251,111,512)(35,147,656,264,405,273,93,182,451)(36,317,535,360,542,703,106,402,163)(37,385,495,277,620,228,206,219,167)(38,487,296,105,642,361,700,267,327)(40,488,142,415,690,604,683,241,425)(41,126,160,298,665,595,525,210,321)(42,574,123,571,365,427,503,246,226)(43,627,314,680,155,325,231,191,578)(44,101,187,445,467,641,663,201,565)(45,460,357,153,511,441,299,661,255)(46,489,63,592,229,462,383,232,399)(47,580,302,189,164,417,447,545,653)(49,295,392,307,294,435,473,686,367)(54,190,320,697,64,577,669,394,104)(55,679,636,543,92,199,518,432,248)(56,490,347,602,396,475,215,162,373)(57,601,501,349,135,650,91,266,240)(58,591,282,336,315,548,324,252,528)(62,311,472,156,303,608,568,305,76)(65,534,340,631,443,238,204,465,527)(66,146,288,119,389,132,207,184,509)(67,456,674,140,150,660,617,242,554)(68,172,312,393,519,522,94,492,567)(69,497,695,329,151,453,539,304,555)(70,379,667,430,130,596,668,108,175)(71,364,541,220,378,234,423,372,318)(77,671,362,86,369,342,177,195,230)(79,390,397,205,556,268,606,498,575)(85,275,286,673,227,244,185,491,461)(89,407,412,297,129,292,272,630,398)(90,643,477,454,559,310,626,180,611)(95,197,658,381,672,143,437,353,652)(96,386,291,113,587,615,224,198,270)(97,560,387,584,646,221,374,452,645)(107,176,635,375,115,313,553,440,269)(109,464,450,599,148,249,531,664,651)(110,281,418,687,637,322,145,557,507)(112,510,271,684,194,380,404,494,280)(116,678,603,614,139,520,470,536,583)(127,670,236,354,149,625,629,659,278)(128,538,699,400,638,416,459,549,676)(133,237,702,529,363,675,233,607,216)(136,436,499,640,377,243,223,446,466)(137,588,429,253,421,287,301,276,585)(138,154,211,433,333,239,214,597,572)(157,474,335,368,481,178,274,530,346)(158,434,628,616,455,420,523,408,655)(161,257,371,685,544,382,344,677,179)(166,426,300,401,424,483,479,202,508)(186,289,250,263,623,504,341,283,414)(192,293,562,610,438,533,594,613,681)(200,624,666,419,260,350,516,600,657)(203,547,521,356,593,493,212,579,569)(213,225,284,285,339,654,442,410,632)(290,406,431,326,355,480,395,633,306),(1,56,187,328,183,529,275,498,331,689,398,491,627,634,152,559,375,94,508)(2,266,83,435,640,52,481,534,176,381,700,472,570,433,329,519,16,234,126)(3,503,587,449,518,505,48,278,686,64,625,202,619,199,662,289,312,212,217)(4,482,192,305,214,461,72,252,540,440,609,296,262,300,171,653,270,393,621)(5,369,46,392,572,455,366,290,584,683,699,668,235,422,408,195,54,115,211)(6,232,655,227,663,356,167,18,215,649,682,359,41,98,405,58,616,553,563)(7,388,437,181,412,197,688,136,694,133,579,387,339,164,57,108,24,681,255)(8,363,471,100,648,110,629,146,659,165,251,516,428,438,376,244,298,228,528)(9,66,382,490,175,96,536,103,646,596,624,603,504,560,370,344,288,297,679)(10,506,238,614,60,470,465,151,564,462,258,426,488,334,242,549,476,618,269)(11,259,466,400,173,658,303,521,660,362,364,248,577,282,399,404,294,277,293)(12,104,73,454,204,487,569,307,475,299,156,467,271,111,515,62,93,280,550)(13,542,492,279,574,575,338,105,14,45,628,65,59,602,631,158,573,203,643)(15,229,576,566,368,114,273,44,578,349,20,558,247,690,233,495,642,190,497)(17,172,81,285,406,106,323,496,514,537,486,391,153,606,159,601,350,246,469)(19,636,337,385,697,319,311,371,256,430,582,68,179,91,26,30,191,509,157)(21,565,351,188,651,656,102,698,241,272,535,113,301,325,250,390,622,538,166)(22,213,135,141,691,78,378,439,347,445,196,652,436,182,644,502,530,657,693)(23,186,424,209,501,170,675,443,144,240,70,346,120,526,670,53,522,76,231)(25,128,429,384,463,343,36,557,647,205,395,701,500,43,425,554,31,116,598)(27,295,90,525,562,638,457,61,419,225,253,147,641,418,318,499,373,107,67)(28,630,477,218,383,50,185,450,548,77,194,216,479,674,661,427,341,47,326)(29,138,599,132,35,678,134,460,583,101,207,99,177,431,261,665,403,620,306)(32,590,607,595,394,608,313,286,473,543,474,333,124,75,494,143,453,604,131)(33,673,539,523,321,265,597,95,532,142,335,635,125,184,79,702,74,402,544)(34,415,198,82,42,145,639,567,666,283,416,551,178,446,302,434,447,612,423)(37,420,84,591,517,677,268,456,594,360,389,547,63,71,459,581,353,230,377)(38,355,511,588,324,411,348,109,703,336,533,513,407,451,605,617,409,123,489)(39,524,637,40,327,696,69,221,239,361,208,332,122,512,121,545,561,245,291)(49,320,414,163,254,160,568,352,276,626,257,267,155,260,380,20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+PGAltOnSets(38,2), +PGSymOnSets(38,2), PGAlt, PGSym, ]; @@ -460,8 +460,8 @@ PGAlt, PGSym, ]; PRIMGRP[715]:=[ 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+PGAltOnSets(13,4), +PGSymOnSets(13,4), PGAlt, PGSym, ]; diff --git a/data/gps7.g b/data/gps7.g index e6d093f..f244126 100644 --- a/data/gps7.g +++ b/data/gps7.g @@ -633,8 +633,8 @@ PGAlt, PGSym, ]; PRIMGRP[741]:=[ 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+PGAltOnSets(39,2), +PGSymOnSets(39,2), PGAlt, PGSym, ]; diff --git a/data/gps8.g b/data/gps8.g index c9643f8..97b2c32 100644 --- a/data/gps8.g +++ b/data/gps8.g @@ -216,8 +216,8 @@ PGAlt, PGSym, ]; PRIMGRP[780]:=[ 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+PGAltOnSets(40,2), +PGSymOnSets(40,2), PGAlt, PGSym, ]; @@ -313,8 +313,8 @@ PGAlt, PGSym, ]; PRIMGRP[792]:=[ 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+PGAltOnSets(12,5), +PGSymOnSets(12,5), PGAlt, PGSym, ]; @@ -459,8 +459,8 @@ PGAlt, PGSym, ]; PRIMGRP[816]:=[ 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+PGAltOnSets(18,3), +PGSymOnSets(18,3), PGAlt, PGSym, ]; @@ -492,8 +492,8 @@ PRIMGRP[820]:=[ [7,6886425600,0,"2",[[90,1],[729,1]],1,"PSp(4, 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diff --git a/data/gps9.g b/data/gps9.g index 3e92bfd..35adaff 100644 --- a/data/gps9.g +++ b/data/gps9.g @@ -83,8 +83,8 @@ PGSym, PRIMGRP[861]:=[ [1,34440,1,"2",[[40,12],[10,2],[20,18]],1,"PSL(2, 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+PGAltOnSets(19,3), +PGSymOnSets(19,3), PGAlt, PGSym, ]; @@ -1019,8 +1019,8 @@ PGAlt, PGSym, ]; PRIMGRP[990]:=[ 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+PGAltOnSets(45,2), +PGSymOnSets(45,2), PGAlt, PGSym, ]; diff --git a/lib/primitiv.gi b/lib/primitiv.gi index b196a90..f7d55fb 100644 --- a/lib/primitiv.gi +++ b/lib/primitiv.gi @@ -51,6 +51,92 @@ BindGlobal("PGSym",function(deg,nr) Concatenation("S(",String(deg),")"), ["A",deg,1], "Sym" ]; end); +############################################################################# +## +#F PGAltOnSets( , ) . . . . Alt(n) and Sym(n) on the k-subsets of [1..n] +#F PGSymOnSets( , ) +## +## Alt(n) and Sym(n) acting on the k-element subsets of [1..n], which is a +## primitive group of degree Binomial(n,k). Like PGPsl and unlike PGAlt these +## take arguments, because the degree alone determines neither n nor k, and +## they return a function of `deg` and `nr` that is inserted as an entry into +## PRIMGRP and invoked by PRIMGrp on first use. +## +## Everything the entry records follows from n and k. Two of the nine fields +## are worth spelling out: +## +## The suborbits are the subdegrees of the Johnson scheme. The stabiliser of +## a k-set S has one orbit for each i = 1..k, holding the k-sets that agree +## with S in all but i of its points: Binomial(k,i) choices of which points of +## S to drop, and Binomial(n-k,i) of what to put in their place. At n = 45, +## k = 2 that is 2*43 = 86 sets sharing a point with S, and 1*903 = 903 +## disjoint from it. +## +## Field 9 is ["sets", , ], where describes the group being +## acted with rather than being it -- here ["Alt",n] or ["Sym",n]. A family +## with a different inner group, such as PSL(2,q) on the 2-subsets of the +## projective line, then wants a case in PRIMGRP_InnerGroup below and not a +## form of its own. +## +BindGlobal("PRIMGRP_JohnsonSuborbits",function(n,k) + return Set(Collected(List([1..k],i->Binomial(k,i)*Binomial(n-k,i)))); +end); + +BindGlobal("PGAltOnSets",function(n,k) + return function(deg,nr) + Assert(0, deg = Binomial(n,k)); + return [ nr, Factorial(n)/2, 1, "2", PRIMGRP_JohnsonSuborbits(n,k), 1, + Concatenation("A(",String(n),")"), ["A",n,1], + ["sets",["Alt",n],k] ]; + end; +end); + +BindGlobal("PGSymOnSets",function(n,k) + return function(deg,nr) + Assert(0, deg = Binomial(n,k)); + return [ nr, Factorial(n), 0, "2", PRIMGRP_JohnsonSuborbits(n,k), 1, + Concatenation("S(",String(n),")"), ["A",n,1], + ["sets",["Sym",n],k] ]; + end; +end); + +############################################################################# +## +#F PGOnSetsGroup( , ) . . . . . . an inner group on the k-subsets +## +## Build the group an entry's field 9 asks for: PRIMGRP_InnerGroup turns the +## description into a group, and PGOnSetsGroup returns its action on +## the k-element subsets of its points. +## +## The action is taken on the orbit of one k-set, so it is the action on all +## of them only if the group is k-homogeneous. A group that is not would give +## a group of the wrong degree rather than an error, so that is checked. +## +## The orbit is sorted before it is acted on. Which permutation group comes +## out depends on the order of the points, and Orbit does not promise one, so +## without this the group would be at the mercy of how Orbit happens to be +## implemented. +## +BindGlobal("PRIMGRP_InnerGroup",function(inner) + if inner[1] = "Alt" then + return AlternatingGroup(inner[2]); + elif inner[1] = "Sym" then + return SymmetricGroup(inner[2]); + fi; + Error("PGOnSetsGroup: unknown inner group ",inner[1]); +end); + +BindGlobal("PGOnSetsGroup",function(inner,k) + local g,pts; + g:=PRIMGRP_InnerGroup(inner); + pts:=Set(Orbit(g,[1..k],OnSets)); + if Length(pts) <> Binomial(NrMovedPoints(g),k) then + Error("PGOnSetsGroup: ",inner[1]," is not ",k,"-homogeneous on ", + NrMovedPoints(g)," points"); + fi; + return Action(g,pts,OnSets); +end); + ############################################################################# ## #F PGPsl( , ) . . . . the natural projective actions of the L series @@ -318,6 +404,8 @@ local l,g,fac,mats,perms,v,t,filename,strm,r,dim,q,k; else g:= PGammaL(dim,q); fi; + elif IsList(l[9]) and Length(l[9]) = 3 and l[9][1] = "sets" then + g:= PGOnSetsGroup(l[9][2], l[9][3]); elif Length(l[9]) = 2 and l[9][1] = "4c" then # product action: the socle width in field 8 gives k, and the degree # its k-th root gives m diff --git a/tst/testinstall/bugfix.tst b/tst/testinstall/bugfix.tst index 5844faa..3d937e7 100644 --- a/tst/testinstall/bugfix.tst +++ b/tst/testinstall/bugfix.tst @@ -155,5 +155,21 @@ gap> List([[25,23],[1000,23]], > [1..p[1]]) ]); [ [ 7200, true ], [ 559872000, true ] ] +# Alt(n) and Sym(n) on the k-subsets are the call PGAltOnSets(n,k) or +# PGSymOnSets(n,k): the order, the transitivity, the socle and the Johnson +# suborbits Binomial(k,i)*Binomial(n-k,i) all follow from n and k, so the entry +# stores none of them. The order is recomputed here rather than read off the +# entry, and the name is checked because it comes from the constructor now +# rather than from the file. +gap> List([[10,1],[35,3],[126,12]], +> p -> [ Name(PrimitiveGroup(p[1],p[2])), +> Size(Group(GeneratorsOfGroup(PrimitiveGroup(p[1],p[2])))), +> Collected(OrbitLengthsDomain( +> Stabilizer(PrimitiveGroup(p[1],p[2]),1), [1..p[1]])) ]); +[ [ "A(5)", 60, [ [ 1, 1 ], [ 3, 1 ], [ 6, 1 ] ] ], + [ "A(7)", 2520, [ [ 1, 1 ], [ 4, 1 ], [ 12, 1 ], [ 18, 1 ] ] ], + [ "A(9)", 181440, [ [ 1, 1 ], [ 5, 1 ], [ 20, 1 ], [ 40, 1 ], [ 60, 1 ] ] ] + ] + # gap> STOP_TEST("bugfix.tst", 1);