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D1868 #16836638
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 471 points:
(1,2,3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471);(2,4)(6,471)(7,470)(8,469)(9,468)(10,467)(11,466)(12,465)(13,464)(14,463)(15,462)(16,461)(17,460)(18,459)(19,458)(20,457)(21,456)(22,455)(23,454)(24,453)(25,452)(26,451)(27,450)(28,449)(29,448)(30,447)(31,446)(32,445)(33,444)(34,443)(35,442)(36,441)(37,440)(38,439)(39,438)(40,437)(41,436)(42,435)(43,434)(44,433)(45,432)(46,431)(47,430)(48,429)(49,428)(50,427)(51,426)(52,425)(53,424)(54,423)(55,422)(56,421)(57,420)(58,419)(59,418)(60,417)(61,416)(62,415)(63,414)(64,413)(65,412)(66,411)(67,410)(68,409)(69,408)(70,407)(71,406)(72,405)(73,404)(74,403)(75,402)(76,401)(77,400)(78,399)(79,398)(80,397)(81,396)(82,395)(83,394)(84,393)(85,392)(86,391)(87,390)(88,389)(89,388)(90,387)(91,386)(92,385)(93,384)(94,383)(95,382)(96,381)(97,380)(98,379)(99,378)(100,377)(101,376)(102,375)(103,374)(104,373)(105,372)(106,371)(107,370)(108,369)(109,368)(110,367)(111,366)(112,365)(113,364)(114,363)(115,362)(116,361)(117,360)(118,359)(119,358)(120,357)(121,356)(122,355)(123,354)(124,353)(125,352)(126,351)(127,350)(128,349)(129,348)(130,347)(131,346)(132,345)(133,344)(134,343)(135,342)(136,341)(137,340)(138,339)(139,338)(140,337)(141,336)(142,335)(143,334)(144,333)(145,332)(146,331)(147,330)(148,329)(149,328)(150,327)(151,326)(152,325)(153,324)(154,323)(155,322)(156,321)(157,320)(158,319)(159,318)(160,317)(161,316)(162,315)(163,314)(164,313)(165,312)(166,311)(167,310)(168,309)(169,308)(170,307)(171,306)(172,305)(173,304)(174,303)(175,302)(176,301)(177,300)(178,299)(179,298)(180,297)(181,296)(182,295)(183,294)(184,293)(185,292)(186,291)(187,290)(188,289)(189,288)(190,287)(191,286)(192,285)(193,284)(194,283)(195,282)(196,281)(197,280)(198,279)(199,278)(200,277)(201,276)(202,275)(203,274)(204,273)(205,272)(206,271)(207,270)(208,269)(209,268)(210,267)(211,266)(212,265)(213,264)(214,263)(215,262)(216,261)(217,260)(218,259)(219,258)(220,257)(221,256)(222,255)(223,254)(224,253)(225,252)(226,251)(227,250)(228,249)(229,248)(230,247)(231,246)(232,245)(233,244)(234,243)(235,242)(236,241)(237,240)(238,239)
Polycyclic presentation:
2^3,467|b^a=bc,d^a=d^466,d^b=d^466
Conjugacy classes & character table
937 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3736, 10);
Finite Group Databasebeta