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D569 #11765870
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 569 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);(2,569)(3,568)(4,567)(5,566)(6,565)(7,564)(8,563)(9,562)(10,561)(11,560)(12,559)(13,558)(14,557)(15,556)(16,555)(17,554)(18,553)(19,552)(20,551)(21,550)(22,549)(23,548)(24,547)(25,546)(26,545)(27,544)(28,543)(29,542)(30,541)(31,540)(32,539)(33,538)(34,537)(35,536)(36,535)(37,534)(38,533)(39,532)(40,531)(41,530)(42,529)(43,528)(44,527)(45,526)(46,525)(47,524)(48,523)(49,522)(50,521)(51,520)(52,519)(53,518)(54,517)(55,516)(56,515)(57,514)(58,513)(59,512)(60,511)(61,510)(62,509)(63,508)(64,507)(65,506)(66,505)(67,504)(68,503)(69,502)(70,501)(71,500)(72,499)(73,498)(74,497)(75,496)(76,495)(77,494)(78,493)(79,492)(80,491)(81,490)(82,489)(83,488)(84,487)(85,486)(86,485)(87,484)(88,483)(89,482)(90,481)(91,480)(92,479)(93,478)(94,477)(95,476)(96,475)(97,474)(98,473)(99,472)(100,471)(101,470)(102,469)(103,468)(104,467)(105,466)(106,465)(107,464)(108,463)(109,462)(110,461)(111,460)(112,459)(113,458)(114,457)(115,456)(116,455)(117,454)(118,453)(119,452)(120,451)(121,450)(122,449)(123,448)(124,447)(125,446)(126,445)(127,444)(128,443)(129,442)(130,441)(131,440)(132,439)(133,438)(134,437)(135,436)(136,435)(137,434)(138,433)(139,432)(140,431)(141,430)(142,429)(143,428)(144,427)(145,426)(146,425)(147,424)(148,423)(149,422)(150,421)(151,420)(152,419)(153,418)(154,417)(155,416)(156,415)(157,414)(158,413)(159,412)(160,411)(161,410)(162,409)(163,408)(164,407)(165,406)(166,405)(167,404)(168,403)(169,402)(170,401)(171,400)(172,399)(173,398)(174,397)(175,396)(176,395)(177,394)(178,393)(179,392)(180,391)(181,390)(182,389)(183,388)(184,387)(185,386)(186,385)(187,384)(188,383)(189,382)(190,381)(191,380)(192,379)(193,378)(194,377)(195,376)(196,375)(197,374)(198,373)(199,372)(200,371)(201,370)(202,369)(203,368)(204,367)(205,366)(206,365)(207,364)(208,363)(209,362)(210,361)(211,360)(212,359)(213,358)(214,357)(215,356)(216,355)(217,354)(218,353)(219,352)(220,351)(221,350)(222,349)(223,348)(224,347)(225,346)(226,345)(227,344)(228,343)(229,342)(230,341)(231,340)(232,339)(233,338)(234,337)(235,336)(236,335)(237,334)(238,333)(239,332)(240,331)(241,330)(242,329)(243,328)(244,327)(245,326)(246,325)(247,324)(248,323)(249,322)(250,321)(251,320)(252,319)(253,318)(254,317)(255,316)(256,315)(257,314)(258,313)(259,312)(260,311)(261,310)(262,309)(263,308)(264,307)(265,306)(266,305)(267,304)(268,303)(269,302)(270,301)(271,300)(272,299)(273,298)(274,297)(275,296)(276,295)(277,294)(278,293)(279,292)(280,291)(281,290)(282,289)(283,288)(284,287)(285,286)
Polycyclic presentation:
2,569|b^a=b^568
Conjugacy classes & character table
286 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1138, 1);
Finite Group Databasebeta