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D7545 #28419045
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 511 points:
(1,2,3)(4,5,6,7,8)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511);(2,3)(5,8)(6,7)(10,511)(11,510)(12,509)(13,508)(14,507)(15,506)(16,505)(17,504)(18,503)(19,502)(20,501)(21,500)(22,499)(23,498)(24,497)(25,496)(26,495)(27,494)(28,493)(29,492)(30,491)(31,490)(32,489)(33,488)(34,487)(35,486)(36,485)(37,484)(38,483)(39,482)(40,481)(41,480)(42,479)(43,478)(44,477)(45,476)(46,475)(47,474)(48,473)(49,472)(50,471)(51,470)(52,469)(53,468)(54,467)(55,466)(56,465)(57,464)(58,463)(59,462)(60,461)(61,460)(62,459)(63,458)(64,457)(65,456)(66,455)(67,454)(68,453)(69,452)(70,451)(71,450)(72,449)(73,448)(74,447)(75,446)(76,445)(77,444)(78,443)(79,442)(80,441)(81,440)(82,439)(83,438)(84,437)(85,436)(86,435)(87,434)(88,433)(89,432)(90,431)(91,430)(92,429)(93,428)(94,427)(95,426)(96,425)(97,424)(98,423)(99,422)(100,421)(101,420)(102,419)(103,418)(104,417)(105,416)(106,415)(107,414)(108,413)(109,412)(110,411)(111,410)(112,409)(113,408)(114,407)(115,406)(116,405)(117,404)(118,403)(119,402)(120,401)(121,400)(122,399)(123,398)(124,397)(125,396)(126,395)(127,394)(128,393)(129,392)(130,391)(131,390)(132,389)(133,388)(134,387)(135,386)(136,385)(137,384)(138,383)(139,382)(140,381)(141,380)(142,379)(143,378)(144,377)(145,376)(146,375)(147,374)(148,373)(149,372)(150,371)(151,370)(152,369)(153,368)(154,367)(155,366)(156,365)(157,364)(158,363)(159,362)(160,361)(161,360)(162,359)(163,358)(164,357)(165,356)(166,355)(167,354)(168,353)(169,352)(170,351)(171,350)(172,349)(173,348)(174,347)(175,346)(176,345)(177,344)(178,343)(179,342)(180,341)(181,340)(182,339)(183,338)(184,337)(185,336)(186,335)(187,334)(188,333)(189,332)(190,331)(191,330)(192,329)(193,328)(194,327)(195,326)(196,325)(197,324)(198,323)(199,322)(200,321)(201,320)(202,319)(203,318)(204,317)(205,316)(206,315)(207,314)(208,313)(209,312)(210,311)(211,310)(212,309)(213,308)(214,307)(215,306)(216,305)(217,304)(218,303)(219,302)(220,301)(221,300)(222,299)(223,298)(224,297)(225,296)(226,295)(227,294)(228,293)(229,292)(230,291)(231,290)(232,289)(233,288)(234,287)(235,286)(236,285)(237,284)(238,283)(239,282)(240,281)(241,280)(242,279)(243,278)(244,277)(245,276)(246,275)(247,274)(248,273)(249,272)(250,271)(251,270)(252,269)(253,268)(254,267)(255,266)(256,265)(257,264)(258,263)(259,262)(260,261)
Polycyclic presentation:
2,3,5,503|b^a=b^2,c^a=c^4,d^a=d^502
Conjugacy classes & character table
3774 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15090, 8);
Finite Group Databasebeta