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D557 #11764339
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 557 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);(2,557)(3,556)(4,555)(5,554)(6,553)(7,552)(8,551)(9,550)(10,549)(11,548)(12,547)(13,546)(14,545)(15,544)(16,543)(17,542)(18,541)(19,540)(20,539)(21,538)(22,537)(23,536)(24,535)(25,534)(26,533)(27,532)(28,531)(29,530)(30,529)(31,528)(32,527)(33,526)(34,525)(35,524)(36,523)(37,522)(38,521)(39,520)(40,519)(41,518)(42,517)(43,516)(44,515)(45,514)(46,513)(47,512)(48,511)(49,510)(50,509)(51,508)(52,507)(53,506)(54,505)(55,504)(56,503)(57,502)(58,501)(59,500)(60,499)(61,498)(62,497)(63,496)(64,495)(65,494)(66,493)(67,492)(68,491)(69,490)(70,489)(71,488)(72,487)(73,486)(74,485)(75,484)(76,483)(77,482)(78,481)(79,480)(80,479)(81,478)(82,477)(83,476)(84,475)(85,474)(86,473)(87,472)(88,471)(89,470)(90,469)(91,468)(92,467)(93,466)(94,465)(95,464)(96,463)(97,462)(98,461)(99,460)(100,459)(101,458)(102,457)(103,456)(104,455)(105,454)(106,453)(107,452)(108,451)(109,450)(110,449)(111,448)(112,447)(113,446)(114,445)(115,444)(116,443)(117,442)(118,441)(119,440)(120,439)(121,438)(122,437)(123,436)(124,435)(125,434)(126,433)(127,432)(128,431)(129,430)(130,429)(131,428)(132,427)(133,426)(134,425)(135,424)(136,423)(137,422)(138,421)(139,420)(140,419)(141,418)(142,417)(143,416)(144,415)(145,414)(146,413)(147,412)(148,411)(149,410)(150,409)(151,408)(152,407)(153,406)(154,405)(155,404)(156,403)(157,402)(158,401)(159,400)(160,399)(161,398)(162,397)(163,396)(164,395)(165,394)(166,393)(167,392)(168,391)(169,390)(170,389)(171,388)(172,387)(173,386)(174,385)(175,384)(176,383)(177,382)(178,381)(179,380)(180,379)(181,378)(182,377)(183,376)(184,375)(185,374)(186,373)(187,372)(188,371)(189,370)(190,369)(191,368)(192,367)(193,366)(194,365)(195,364)(196,363)(197,362)(198,361)(199,360)(200,359)(201,358)(202,357)(203,356)(204,355)(205,354)(206,353)(207,352)(208,351)(209,350)(210,349)(211,348)(212,347)(213,346)(214,345)(215,344)(216,343)(217,342)(218,341)(219,340)(220,339)(221,338)(222,337)(223,336)(224,335)(225,334)(226,333)(227,332)(228,331)(229,330)(230,329)(231,328)(232,327)(233,326)(234,325)(235,324)(236,323)(237,322)(238,321)(239,320)(240,319)(241,318)(242,317)(243,316)(244,315)(245,314)(246,313)(247,312)(248,311)(249,310)(250,309)(251,308)(252,307)(253,306)(254,305)(255,304)(256,303)(257,302)(258,301)(259,300)(260,299)(261,298)(262,297)(263,296)(264,295)(265,294)(266,293)(267,292)(268,291)(269,290)(270,289)(271,288)(272,287)(273,286)(274,285)(275,284)(276,283)(277,282)(278,281)(279,280)
Polycyclic presentation:
2,557|b^a=b^556
Conjugacy classes & character table
280 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1114, 1);
Finite Group Databasebeta