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Aliases
Splittings
Subgroups
60 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 539 points:
(1,2)(3,4,5)(6,7,8,9,10)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539);(4,5)(7,10)(8,9)(12,539)(13,538)(14,537)(15,536)(16,535)(17,534)(18,533)(19,532)(20,531)(21,530)(22,529)(23,528)(24,527)(25,526)(26,525)(27,524)(28,523)(29,522)(30,521)(31,520)(32,519)(33,518)(34,517)(35,516)(36,515)(37,514)(38,513)(39,512)(40,511)(41,510)(42,509)(43,508)(44,507)(45,506)(46,505)(47,504)(48,503)(49,502)(50,501)(51,500)(52,499)(53,498)(54,497)(55,496)(56,495)(57,494)(58,493)(59,492)(60,491)(61,490)(62,489)(63,488)(64,487)(65,486)(66,485)(67,484)(68,483)(69,482)(70,481)(71,480)(72,479)(73,478)(74,477)(75,476)(76,475)(77,474)(78,473)(79,472)(80,471)(81,470)(82,469)(83,468)(84,467)(85,466)(86,465)(87,464)(88,463)(89,462)(90,461)(91,460)(92,459)(93,458)(94,457)(95,456)(96,455)(97,454)(98,453)(99,452)(100,451)(101,450)(102,449)(103,448)(104,447)(105,446)(106,445)(107,444)(108,443)(109,442)(110,441)(111,440)(112,439)(113,438)(114,437)(115,436)(116,435)(117,434)(118,433)(119,432)(120,431)(121,430)(122,429)(123,428)(124,427)(125,426)(126,425)(127,424)(128,423)(129,422)(130,421)(131,420)(132,419)(133,418)(134,417)(135,416)(136,415)(137,414)(138,413)(139,412)(140,411)(141,410)(142,409)(143,408)(144,407)(145,406)(146,405)(147,404)(148,403)(149,402)(150,401)(151,400)(152,399)(153,398)(154,397)(155,396)(156,395)(157,394)(158,393)(159,392)(160,391)(161,390)(162,389)(163,388)(164,387)(165,386)(166,385)(167,384)(168,383)(169,382)(170,381)(171,380)(172,379)(173,378)(174,377)(175,376)(176,375)(177,374)(178,373)(179,372)(180,371)(181,370)(182,369)(183,368)(184,367)(185,366)(186,365)(187,364)(188,363)(189,362)(190,361)(191,360)(192,359)(193,358)(194,357)(195,356)(196,355)(197,354)(198,353)(199,352)(200,351)(201,350)(202,349)(203,348)(204,347)(205,346)(206,345)(207,344)(208,343)(209,342)(210,341)(211,340)(212,339)(213,338)(214,337)(215,336)(216,335)(217,334)(218,333)(219,332)(220,331)(221,330)(222,329)(223,328)(224,327)(225,326)(226,325)(227,324)(228,323)(229,322)(230,321)(231,320)(232,319)(233,318)(234,317)(235,316)(236,315)(237,314)(238,313)(239,312)(240,311)(241,310)(242,309)(243,308)(244,307)(245,306)(246,305)(247,304)(248,303)(249,302)(250,301)(251,300)(252,299)(253,298)(254,297)(255,296)(256,295)(257,294)(258,293)(259,292)(260,291)(261,290)(262,289)(263,288)(264,287)(265,286)(266,285)(267,284)(268,283)(269,282)(270,281)(271,280)(272,279)(273,278)(274,277)(275,276)
Conjugacy classes & character table
7938 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 28);
Finite Group Databasebeta