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D1461 #15668596
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 490 points:
(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490);(2,3)(5,490)(6,489)(7,488)(8,487)(9,486)(10,485)(11,484)(12,483)(13,482)(14,481)(15,480)(16,479)(17,478)(18,477)(19,476)(20,475)(21,474)(22,473)(23,472)(24,471)(25,470)(26,469)(27,468)(28,467)(29,466)(30,465)(31,464)(32,463)(33,462)(34,461)(35,460)(36,459)(37,458)(38,457)(39,456)(40,455)(41,454)(42,453)(43,452)(44,451)(45,450)(46,449)(47,448)(48,447)(49,446)(50,445)(51,444)(52,443)(53,442)(54,441)(55,440)(56,439)(57,438)(58,437)(59,436)(60,435)(61,434)(62,433)(63,432)(64,431)(65,430)(66,429)(67,428)(68,427)(69,426)(70,425)(71,424)(72,423)(73,422)(74,421)(75,420)(76,419)(77,418)(78,417)(79,416)(80,415)(81,414)(82,413)(83,412)(84,411)(85,410)(86,409)(87,408)(88,407)(89,406)(90,405)(91,404)(92,403)(93,402)(94,401)(95,400)(96,399)(97,398)(98,397)(99,396)(100,395)(101,394)(102,393)(103,392)(104,391)(105,390)(106,389)(107,388)(108,387)(109,386)(110,385)(111,384)(112,383)(113,382)(114,381)(115,380)(116,379)(117,378)(118,377)(119,376)(120,375)(121,374)(122,373)(123,372)(124,371)(125,370)(126,369)(127,368)(128,367)(129,366)(130,365)(131,364)(132,363)(133,362)(134,361)(135,360)(136,359)(137,358)(138,357)(139,356)(140,355)(141,354)(142,353)(143,352)(144,351)(145,350)(146,349)(147,348)(148,347)(149,346)(150,345)(151,344)(152,343)(153,342)(154,341)(155,340)(156,339)(157,338)(158,337)(159,336)(160,335)(161,334)(162,333)(163,332)(164,331)(165,330)(166,329)(167,328)(168,327)(169,326)(170,325)(171,324)(172,323)(173,322)(174,321)(175,320)(176,319)(177,318)(178,317)(179,316)(180,315)(181,314)(182,313)(183,312)(184,311)(185,310)(186,309)(187,308)(188,307)(189,306)(190,305)(191,304)(192,303)(193,302)(194,301)(195,300)(196,299)(197,298)(198,297)(199,296)(200,295)(201,294)(202,293)(203,292)(204,291)(205,290)(206,289)(207,288)(208,287)(209,286)(210,285)(211,284)(212,283)(213,282)(214,281)(215,280)(216,279)(217,278)(218,277)(219,276)(220,275)(221,274)(222,273)(223,272)(224,271)(225,270)(226,269)(227,268)(228,267)(229,266)(230,265)(231,264)(232,263)(233,262)(234,261)(235,260)(236,259)(237,258)(238,257)(239,256)(240,255)(241,254)(242,253)(243,252)(244,251)(245,250)(246,249)(247,248)
Polycyclic presentation:
2,3,487|b^a=b^2,c^a=c^486
Conjugacy classes & character table
732 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2922, 5);
Finite Group Databasebeta