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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 586 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);(4,9)(5,8)(6,7)(11,586)(12,585)(13,584)(14,583)(15,582)(16,581)(17,580)(18,579)(19,578)(20,577)(21,576)(22,575)(23,574)(24,573)(25,572)(26,571)(27,570)(28,569)(29,568)(30,567)(31,566)(32,565)(33,564)(34,563)(35,562)(36,561)(37,560)(38,559)(39,558)(40,557)(41,556)(42,555)(43,554)(44,553)(45,552)(46,551)(47,550)(48,549)(49,548)(50,547)(51,546)(52,545)(53,544)(54,543)(55,542)(56,541)(57,540)(58,539)(59,538)(60,537)(61,536)(62,535)(63,534)(64,533)(65,532)(66,531)(67,530)(68,529)(69,528)(70,527)(71,526)(72,525)(73,524)(74,523)(75,522)(76,521)(77,520)(78,519)(79,518)(80,517)(81,516)(82,515)(83,514)(84,513)(85,512)(86,511)(87,510)(88,509)(89,508)(90,507)(91,506)(92,505)(93,504)(94,503)(95,502)(96,501)(97,500)(98,499)(99,498)(100,497)(101,496)(102,495)(103,494)(104,493)(105,492)(106,491)(107,490)(108,489)(109,488)(110,487)(111,486)(112,485)(113,484)(114,483)(115,482)(116,481)(117,480)(118,479)(119,478)(120,477)(121,476)(122,475)(123,474)(124,473)(125,472)(126,471)(127,470)(128,469)(129,468)(130,467)(131,466)(132,465)(133,464)(134,463)(135,462)(136,461)(137,460)(138,459)(139,458)(140,457)(141,456)(142,455)(143,454)(144,453)(145,452)(146,451)(147,450)(148,449)(149,448)(150,447)(151,446)(152,445)(153,444)(154,443)(155,442)(156,441)(157,440)(158,439)(159,438)(160,437)(161,436)(162,435)(163,434)(164,433)(165,432)(166,431)(167,430)(168,429)(169,428)(170,427)(171,426)(172,425)(173,424)(174,423)(175,422)(176,421)(177,420)(178,419)(179,418)(180,417)(181,416)(182,415)(183,414)(184,413)(185,412)(186,411)(187,410)(188,409)(189,408)(190,407)(191,406)(192,405)(193,404)(194,403)(195,402)(196,401)(197,400)(198,399)(199,398)(200,397)(201,396)(202,395)(203,394)(204,393)(205,392)(206,391)(207,390)(208,389)(209,388)(210,387)(211,386)(212,385)(213,384)(214,383)(215,382)(216,381)(217,380)(218,379)(219,378)(220,377)(221,376)(222,375)(223,374)(224,373)(225,372)(226,371)(227,370)(228,369)(229,368)(230,367)(231,366)(232,365)(233,364)(234,363)(235,362)(236,361)(237,360)(238,359)(239,358)(240,357)(241,356)(242,355)(243,354)(244,353)(245,352)(246,351)(247,350)(248,349)(249,348)(250,347)(251,346)(252,345)(253,344)(254,343)(255,342)(256,341)(257,340)(258,339)(259,338)(260,337)(261,336)(262,335)(263,334)(264,333)(265,332)(266,331)(267,330)(268,329)(269,328)(270,327)(271,326)(272,325)(273,324)(274,323)(275,322)(276,321)(277,320)(278,319)(279,318)(280,317)(281,316)(282,315)(283,314)(284,313)(285,312)(286,311)(287,310)(288,309)(289,308)(290,307)(291,306)(292,305)(293,304)(294,303)(295,302)(296,301)(297,300)(298,299)
Conjugacy classes & character table
4042 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16156, 9);
Finite Group Databasebeta