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Dic4390 #72215829
Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 452 points:
(1,2,3,4)(5,8,7,6)(9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452);(1,5,3,7)(2,6,4,8)(10,13)(11,12)(15,452)(16,451)(17,450)(18,449)(19,448)(20,447)(21,446)(22,445)(23,444)(24,443)(25,442)(26,441)(27,440)(28,439)(29,438)(30,437)(31,436)(32,435)(33,434)(34,433)(35,432)(36,431)(37,430)(38,429)(39,428)(40,427)(41,426)(42,425)(43,424)(44,423)(45,422)(46,421)(47,420)(48,419)(49,418)(50,417)(51,416)(52,415)(53,414)(54,413)(55,412)(56,411)(57,410)(58,409)(59,408)(60,407)(61,406)(62,405)(63,404)(64,403)(65,402)(66,401)(67,400)(68,399)(69,398)(70,397)(71,396)(72,395)(73,394)(74,393)(75,392)(76,391)(77,390)(78,389)(79,388)(80,387)(81,386)(82,385)(83,384)(84,383)(85,382)(86,381)(87,380)(88,379)(89,378)(90,377)(91,376)(92,375)(93,374)(94,373)(95,372)(96,371)(97,370)(98,369)(99,368)(100,367)(101,366)(102,365)(103,364)(104,363)(105,362)(106,361)(107,360)(108,359)(109,358)(110,357)(111,356)(112,355)(113,354)(114,353)(115,352)(116,351)(117,350)(118,349)(119,348)(120,347)(121,346)(122,345)(123,344)(124,343)(125,342)(126,341)(127,340)(128,339)(129,338)(130,337)(131,336)(132,335)(133,334)(134,333)(135,332)(136,331)(137,330)(138,329)(139,328)(140,327)(141,326)(142,325)(143,324)(144,323)(145,322)(146,321)(147,320)(148,319)(149,318)(150,317)(151,316)(152,315)(153,314)(154,313)(155,312)(156,311)(157,310)(158,309)(159,308)(160,307)(161,306)(162,305)(163,304)(164,303)(165,302)(166,301)(167,300)(168,299)(169,298)(170,297)(171,296)(172,295)(173,294)(174,293)(175,292)(176,291)(177,290)(178,289)(179,288)(180,287)(181,286)(182,285)(183,284)(184,283)(185,282)(186,281)(187,280)(188,279)(189,278)(190,277)(191,276)(192,275)(193,274)(194,273)(195,272)(196,271)(197,270)(198,269)(199,268)(200,267)(201,266)(202,265)(203,264)(204,263)(205,262)(206,261)(207,260)(208,259)(209,258)(210,257)(211,256)(212,255)(213,254)(214,253)(215,252)(216,251)(217,250)(218,249)(219,248)(220,247)(221,246)(222,245)(223,244)(224,243)(225,242)(226,241)(227,240)(228,239)(229,238)(230,237)(231,236)(232,235)(233,234)
Polycyclic presentation:
2^3,5,439|a^2=c,b^2=c,b^a=bc,d^a=d^4,e^a=e^438
Conjugacy classes & character table
4393 conjugacy classes. The character table is too large to display.
Relationships
GAP
Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:
gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e");;
gap> coll := SingleCollector(F, [2, 2, 2, 5, 439]);;
gap> SetPower(coll, 1, F.3);;
gap> SetPower(coll, 2, F.3);;
gap> SetConjugate(coll, 2, 1, F.2*F.3);;
gap> SetConjugate(coll, 4, 1, F.4^4);;
gap> SetConjugate(coll, 5, 1, F.5^438);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);
Finite Group Databasebeta