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Dic7999 #44544600
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 444 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);(1,3,2,4)(6,23)(7,22)(8,21)(9,20)(10,19)(11,18)(12,17)(13,16)(14,15)(25,444)(26,443)(27,442)(28,441)(29,440)(30,439)(31,438)(32,437)(33,436)(34,435)(35,434)(36,433)(37,432)(38,431)(39,430)(40,429)(41,428)(42,427)(43,426)(44,425)(45,424)(46,423)(47,422)(48,421)(49,420)(50,419)(51,418)(52,417)(53,416)(54,415)(55,414)(56,413)(57,412)(58,411)(59,410)(60,409)(61,408)(62,407)(63,406)(64,405)(65,404)(66,403)(67,402)(68,401)(69,400)(70,399)(71,398)(72,397)(73,396)(74,395)(75,394)(76,393)(77,392)(78,391)(79,390)(80,389)(81,388)(82,387)(83,386)(84,385)(85,384)(86,383)(87,382)(88,381)(89,380)(90,379)(91,378)(92,377)(93,376)(94,375)(95,374)(96,373)(97,372)(98,371)(99,370)(100,369)(101,368)(102,367)(103,366)(104,365)(105,364)(106,363)(107,362)(108,361)(109,360)(110,359)(111,358)(112,357)(113,356)(114,355)(115,354)(116,353)(117,352)(118,351)(119,350)(120,349)(121,348)(122,347)(123,346)(124,345)(125,344)(126,343)(127,342)(128,341)(129,340)(130,339)(131,338)(132,337)(133,336)(134,335)(135,334)(136,333)(137,332)(138,331)(139,330)(140,329)(141,328)(142,327)(143,326)(144,325)(145,324)(146,323)(147,322)(148,321)(149,320)(150,319)(151,318)(152,317)(153,316)(154,315)(155,314)(156,313)(157,312)(158,311)(159,310)(160,309)(161,308)(162,307)(163,306)(164,305)(165,304)(166,303)(167,302)(168,301)(169,300)(170,299)(171,298)(172,297)(173,296)(174,295)(175,294)(176,293)(177,292)(178,291)(179,290)(180,289)(181,288)(182,287)(183,286)(184,285)(185,284)(186,283)(187,282)(188,281)(189,280)(190,279)(191,278)(192,277)(193,276)(194,275)(195,274)(196,273)(197,272)(198,271)(199,270)(200,269)(201,268)(202,267)(203,266)(204,265)(205,264)(206,263)(207,262)(208,261)(209,260)(210,259)(211,258)(212,257)(213,256)(214,255)(215,254)(216,253)(217,252)(218,251)(219,250)(220,249)(221,248)(222,247)(223,246)(224,245)(225,244)(226,243)(227,242)(228,241)(229,240)(230,239)(231,238)(232,237)(233,236)(234,235)
Polycyclic presentation:
2,19,421,2|a^2=d,b^a=b^18,c^a=c^420
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, 4);
Finite Group Databasebeta