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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 442 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);(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)(23,442)(24,441)(25,440)(26,439)(27,438)(28,437)(29,436)(30,435)(31,434)(32,433)(33,432)(34,431)(35,430)(36,429)(37,428)(38,427)(39,426)(40,425)(41,424)(42,423)(43,422)(44,421)(45,420)(46,419)(47,418)(48,417)(49,416)(50,415)(51,414)(52,413)(53,412)(54,411)(55,410)(56,409)(57,408)(58,407)(59,406)(60,405)(61,404)(62,403)(63,402)(64,401)(65,400)(66,399)(67,398)(68,397)(69,396)(70,395)(71,394)(72,393)(73,392)(74,391)(75,390)(76,389)(77,388)(78,387)(79,386)(80,385)(81,384)(82,383)(83,382)(84,381)(85,380)(86,379)(87,378)(88,377)(89,376)(90,375)(91,374)(92,373)(93,372)(94,371)(95,370)(96,369)(97,368)(98,367)(99,366)(100,365)(101,364)(102,363)(103,362)(104,361)(105,360)(106,359)(107,358)(108,357)(109,356)(110,355)(111,354)(112,353)(113,352)(114,351)(115,350)(116,349)(117,348)(118,347)(119,346)(120,345)(121,344)(122,343)(123,342)(124,341)(125,340)(126,339)(127,338)(128,337)(129,336)(130,335)(131,334)(132,333)(133,332)(134,331)(135,330)(136,329)(137,328)(138,327)(139,326)(140,325)(141,324)(142,323)(143,322)(144,321)(145,320)(146,319)(147,318)(148,317)(149,316)(150,315)(151,314)(152,313)(153,312)(154,311)(155,310)(156,309)(157,308)(158,307)(159,306)(160,305)(161,304)(162,303)(163,302)(164,301)(165,300)(166,299)(167,298)(168,297)(169,296)(170,295)(171,294)(172,293)(173,292)(174,291)(175,290)(176,289)(177,288)(178,287)(179,286)(180,285)(181,284)(182,283)(183,282)(184,281)(185,280)(186,279)(187,278)(188,277)(189,276)(190,275)(191,274)(192,273)(193,272)(194,271)(195,270)(196,269)(197,268)(198,267)(199,266)(200,265)(201,264)(202,263)(203,262)(204,261)(205,260)(206,259)(207,258)(208,257)(209,256)(210,255)(211,254)(212,253)(213,252)(214,251)(215,250)(216,249)(217,248)(218,247)(219,246)(220,245)(221,244)(222,243)(223,242)(224,241)(225,240)(226,239)(227,238)(228,237)(229,236)(230,235)(231,234)(232,233)
Conjugacy classes & character table
8002 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31996, 11);
Finite Group Databasebeta