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Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 610 points:
(1,2)(3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610);(4,11)(5,10)(6,9)(7,8)(13,610)(14,609)(15,608)(16,607)(17,606)(18,605)(19,604)(20,603)(21,602)(22,601)(23,600)(24,599)(25,598)(26,597)(27,596)(28,595)(29,594)(30,593)(31,592)(32,591)(33,590)(34,589)(35,588)(36,587)(37,586)(38,585)(39,584)(40,583)(41,582)(42,581)(43,580)(44,579)(45,578)(46,577)(47,576)(48,575)(49,574)(50,573)(51,572)(52,571)(53,570)(54,569)(55,568)(56,567)(57,566)(58,565)(59,564)(60,563)(61,562)(62,561)(63,560)(64,559)(65,558)(66,557)(67,556)(68,555)(69,554)(70,553)(71,552)(72,551)(73,550)(74,549)(75,548)(76,547)(77,546)(78,545)(79,544)(80,543)(81,542)(82,541)(83,540)(84,539)(85,538)(86,537)(87,536)(88,535)(89,534)(90,533)(91,532)(92,531)(93,530)(94,529)(95,528)(96,527)(97,526)(98,525)(99,524)(100,523)(101,522)(102,521)(103,520)(104,519)(105,518)(106,517)(107,516)(108,515)(109,514)(110,513)(111,512)(112,511)(113,510)(114,509)(115,508)(116,507)(117,506)(118,505)(119,504)(120,503)(121,502)(122,501)(123,500)(124,499)(125,498)(126,497)(127,496)(128,495)(129,494)(130,493)(131,492)(132,491)(133,490)(134,489)(135,488)(136,487)(137,486)(138,485)(139,484)(140,483)(141,482)(142,481)(143,480)(144,479)(145,478)(146,477)(147,476)(148,475)(149,474)(150,473)(151,472)(152,471)(153,470)(154,469)(155,468)(156,467)(157,466)(158,465)(159,464)(160,463)(161,462)(162,461)(163,460)(164,459)(165,458)(166,457)(167,456)(168,455)(169,454)(170,453)(171,452)(172,451)(173,450)(174,449)(175,448)(176,447)(177,446)(178,445)(179,444)(180,443)(181,442)(182,441)(183,440)(184,439)(185,438)(186,437)(187,436)(188,435)(189,434)(190,433)(191,432)(192,431)(193,430)(194,429)(195,428)(196,427)(197,426)(198,425)(199,424)(200,423)(201,422)(202,421)(203,420)(204,419)(205,418)(206,417)(207,416)(208,415)(209,414)(210,413)(211,412)(212,411)(213,410)(214,409)(215,408)(216,407)(217,406)(218,405)(219,404)(220,403)(221,402)(222,401)(223,400)(224,399)(225,398)(226,397)(227,396)(228,395)(229,394)(230,393)(231,392)(232,391)(233,390)(234,389)(235,388)(236,387)(237,386)(238,385)(239,384)(240,383)(241,382)(242,381)(243,380)(244,379)(245,378)(246,377)(247,376)(248,375)(249,374)(250,373)(251,372)(252,371)(253,370)(254,369)(255,368)(256,367)(257,366)(258,365)(259,364)(260,363)(261,362)(262,361)(263,360)(264,359)(265,358)(266,357)(267,356)(268,355)(269,354)(270,353)(271,352)(272,351)(273,350)(274,349)(275,348)(276,347)(277,346)(278,345)(279,344)(280,343)(281,342)(282,341)(283,340)(284,339)(285,338)(286,337)(287,336)(288,335)(289,334)(290,333)(291,332)(292,331)(293,330)(294,329)(295,328)(296,327)(297,326)(298,325)(299,324)(300,323)(301,322)(302,321)(303,320)(304,319)(305,318)(306,317)(307,316)(308,315)(309,314)(310,313)(311,312)
Conjugacy classes & character table
5394 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21564, 8);
Finite Group Databasebeta