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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 622 points:
(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622);(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(17,622)(18,621)(19,620)(20,619)(21,618)(22,617)(23,616)(24,615)(25,614)(26,613)(27,612)(28,611)(29,610)(30,609)(31,608)(32,607)(33,606)(34,605)(35,604)(36,603)(37,602)(38,601)(39,600)(40,599)(41,598)(42,597)(43,596)(44,595)(45,594)(46,593)(47,592)(48,591)(49,590)(50,589)(51,588)(52,587)(53,586)(54,585)(55,584)(56,583)(57,582)(58,581)(59,580)(60,579)(61,578)(62,577)(63,576)(64,575)(65,574)(66,573)(67,572)(68,571)(69,570)(70,569)(71,568)(72,567)(73,566)(74,565)(75,564)(76,563)(77,562)(78,561)(79,560)(80,559)(81,558)(82,557)(83,556)(84,555)(85,554)(86,553)(87,552)(88,551)(89,550)(90,549)(91,548)(92,547)(93,546)(94,545)(95,544)(96,543)(97,542)(98,541)(99,540)(100,539)(101,538)(102,537)(103,536)(104,535)(105,534)(106,533)(107,532)(108,531)(109,530)(110,529)(111,528)(112,527)(113,526)(114,525)(115,524)(116,523)(117,522)(118,521)(119,520)(120,519)(121,518)(122,517)(123,516)(124,515)(125,514)(126,513)(127,512)(128,511)(129,510)(130,509)(131,508)(132,507)(133,506)(134,505)(135,504)(136,503)(137,502)(138,501)(139,500)(140,499)(141,498)(142,497)(143,496)(144,495)(145,494)(146,493)(147,492)(148,491)(149,490)(150,489)(151,488)(152,487)(153,486)(154,485)(155,484)(156,483)(157,482)(158,481)(159,480)(160,479)(161,478)(162,477)(163,476)(164,475)(165,474)(166,473)(167,472)(168,471)(169,470)(170,469)(171,468)(172,467)(173,466)(174,465)(175,464)(176,463)(177,462)(178,461)(179,460)(180,459)(181,458)(182,457)(183,456)(184,455)(185,454)(186,453)(187,452)(188,451)(189,450)(190,449)(191,448)(192,447)(193,446)(194,445)(195,444)(196,443)(197,442)(198,441)(199,440)(200,439)(201,438)(202,437)(203,436)(204,435)(205,434)(206,433)(207,432)(208,431)(209,430)(210,429)(211,428)(212,427)(213,426)(214,425)(215,424)(216,423)(217,422)(218,421)(219,420)(220,419)(221,418)(222,417)(223,416)(224,415)(225,414)(226,413)(227,412)(228,411)(229,410)(230,409)(231,408)(232,407)(233,406)(234,405)(235,404)(236,403)(237,402)(238,401)(239,400)(240,399)(241,398)(242,397)(243,396)(244,395)(245,394)(246,393)(247,392)(248,391)(249,390)(250,389)(251,388)(252,387)(253,386)(254,385)(255,384)(256,383)(257,382)(258,381)(259,380)(260,379)(261,378)(262,377)(263,376)(264,375)(265,374)(266,373)(267,372)(268,371)(269,370)(270,369)(271,368)(272,367)(273,366)(274,365)(275,364)(276,363)(277,362)(278,361)(279,360)(280,359)(281,358)(282,357)(283,356)(284,355)(285,354)(286,353)(287,352)(288,351)(289,350)(290,349)(291,348)(292,347)(293,346)(294,345)(295,344)(296,343)(297,342)(298,341)(299,340)(300,339)(301,338)(302,337)(303,336)(304,335)(305,334)(306,333)(307,332)(308,331)(309,330)(310,329)(311,328)(312,327)(313,326)(314,325)(315,324)(316,323)(317,322)(318,321)(319,320)
Conjugacy classes & character table
7894 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31564, 11);
Finite Group Databasebeta