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Aliases
Splittings
Subgroups
20 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 596 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);(4,9)(5,8)(6,7)(11,596)(12,595)(13,594)(14,593)(15,592)(16,591)(17,590)(18,589)(19,588)(20,587)(21,586)(22,585)(23,584)(24,583)(25,582)(26,581)(27,580)(28,579)(29,578)(30,577)(31,576)(32,575)(33,574)(34,573)(35,572)(36,571)(37,570)(38,569)(39,568)(40,567)(41,566)(42,565)(43,564)(44,563)(45,562)(46,561)(47,560)(48,559)(49,558)(50,557)(51,556)(52,555)(53,554)(54,553)(55,552)(56,551)(57,550)(58,549)(59,548)(60,547)(61,546)(62,545)(63,544)(64,543)(65,542)(66,541)(67,540)(68,539)(69,538)(70,537)(71,536)(72,535)(73,534)(74,533)(75,532)(76,531)(77,530)(78,529)(79,528)(80,527)(81,526)(82,525)(83,524)(84,523)(85,522)(86,521)(87,520)(88,519)(89,518)(90,517)(91,516)(92,515)(93,514)(94,513)(95,512)(96,511)(97,510)(98,509)(99,508)(100,507)(101,506)(102,505)(103,504)(104,503)(105,502)(106,501)(107,500)(108,499)(109,498)(110,497)(111,496)(112,495)(113,494)(114,493)(115,492)(116,491)(117,490)(118,489)(119,488)(120,487)(121,486)(122,485)(123,484)(124,483)(125,482)(126,481)(127,480)(128,479)(129,478)(130,477)(131,476)(132,475)(133,474)(134,473)(135,472)(136,471)(137,470)(138,469)(139,468)(140,467)(141,466)(142,465)(143,464)(144,463)(145,462)(146,461)(147,460)(148,459)(149,458)(150,457)(151,456)(152,455)(153,454)(154,453)(155,452)(156,451)(157,450)(158,449)(159,448)(160,447)(161,446)(162,445)(163,444)(164,443)(165,442)(166,441)(167,440)(168,439)(169,438)(170,437)(171,436)(172,435)(173,434)(174,433)(175,432)(176,431)(177,430)(178,429)(179,428)(180,427)(181,426)(182,425)(183,424)(184,423)(185,422)(186,421)(187,420)(188,419)(189,418)(190,417)(191,416)(192,415)(193,414)(194,413)(195,412)(196,411)(197,410)(198,409)(199,408)(200,407)(201,406)(202,405)(203,404)(204,403)(205,402)(206,401)(207,400)(208,399)(209,398)(210,397)(211,396)(212,395)(213,394)(214,393)(215,392)(216,391)(217,390)(218,389)(219,388)(220,387)(221,386)(222,385)(223,384)(224,383)(225,382)(226,381)(227,380)(228,379)(229,378)(230,377)(231,376)(232,375)(233,374)(234,373)(235,372)(236,371)(237,370)(238,369)(239,368)(240,367)(241,366)(242,365)(243,364)(244,363)(245,362)(246,361)(247,360)(248,359)(249,358)(250,357)(251,356)(252,355)(253,354)(254,353)(255,352)(256,351)(257,350)(258,349)(259,348)(260,347)(261,346)(262,345)(263,344)(264,343)(265,342)(266,341)(267,340)(268,339)(269,338)(270,337)(271,336)(272,335)(273,334)(274,333)(275,332)(276,331)(277,330)(278,329)(279,328)(280,327)(281,326)(282,325)(283,324)(284,323)(285,322)(286,321)(287,320)(288,319)(289,318)(290,317)(291,316)(292,315)(293,314)(294,313)(295,312)(296,311)(297,310)(298,309)(299,308)(300,307)(301,306)(302,305)(303,304)
Conjugacy classes & character table
4112 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16436, 7);
Finite Group Databasebeta