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Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 670 points:
(1,2)(3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670);(4,11)(5,10)(6,9)(7,8)(13,670)(14,669)(15,668)(16,667)(17,666)(18,665)(19,664)(20,663)(21,662)(22,661)(23,660)(24,659)(25,658)(26,657)(27,656)(28,655)(29,654)(30,653)(31,652)(32,651)(33,650)(34,649)(35,648)(36,647)(37,646)(38,645)(39,644)(40,643)(41,642)(42,641)(43,640)(44,639)(45,638)(46,637)(47,636)(48,635)(49,634)(50,633)(51,632)(52,631)(53,630)(54,629)(55,628)(56,627)(57,626)(58,625)(59,624)(60,623)(61,622)(62,621)(63,620)(64,619)(65,618)(66,617)(67,616)(68,615)(69,614)(70,613)(71,612)(72,611)(73,610)(74,609)(75,608)(76,607)(77,606)(78,605)(79,604)(80,603)(81,602)(82,601)(83,600)(84,599)(85,598)(86,597)(87,596)(88,595)(89,594)(90,593)(91,592)(92,591)(93,590)(94,589)(95,588)(96,587)(97,586)(98,585)(99,584)(100,583)(101,582)(102,581)(103,580)(104,579)(105,578)(106,577)(107,576)(108,575)(109,574)(110,573)(111,572)(112,571)(113,570)(114,569)(115,568)(116,567)(117,566)(118,565)(119,564)(120,563)(121,562)(122,561)(123,560)(124,559)(125,558)(126,557)(127,556)(128,555)(129,554)(130,553)(131,552)(132,551)(133,550)(134,549)(135,548)(136,547)(137,546)(138,545)(139,544)(140,543)(141,542)(142,541)(143,540)(144,539)(145,538)(146,537)(147,536)(148,535)(149,534)(150,533)(151,532)(152,531)(153,530)(154,529)(155,528)(156,527)(157,526)(158,525)(159,524)(160,523)(161,522)(162,521)(163,520)(164,519)(165,518)(166,517)(167,516)(168,515)(169,514)(170,513)(171,512)(172,511)(173,510)(174,509)(175,508)(176,507)(177,506)(178,505)(179,504)(180,503)(181,502)(182,501)(183,500)(184,499)(185,498)(186,497)(187,496)(188,495)(189,494)(190,493)(191,492)(192,491)(193,490)(194,489)(195,488)(196,487)(197,486)(198,485)(199,484)(200,483)(201,482)(202,481)(203,480)(204,479)(205,478)(206,477)(207,476)(208,475)(209,474)(210,473)(211,472)(212,471)(213,470)(214,469)(215,468)(216,467)(217,466)(218,465)(219,464)(220,463)(221,462)(222,461)(223,460)(224,459)(225,458)(226,457)(227,456)(228,455)(229,454)(230,453)(231,452)(232,451)(233,450)(234,449)(235,448)(236,447)(237,446)(238,445)(239,444)(240,443)(241,442)(242,441)(243,440)(244,439)(245,438)(246,437)(247,436)(248,435)(249,434)(250,433)(251,432)(252,431)(253,430)(254,429)(255,428)(256,427)(257,426)(258,425)(259,424)(260,423)(261,422)(262,421)(263,420)(264,419)(265,418)(266,417)(267,416)(268,415)(269,414)(270,413)(271,412)(272,411)(273,410)(274,409)(275,408)(276,407)(277,406)(278,405)(279,404)(280,403)(281,402)(282,401)(283,400)(284,399)(285,398)(286,397)(287,396)(288,395)(289,394)(290,393)(291,392)(292,391)(293,390)(294,389)(295,388)(296,387)(297,386)(298,385)(299,384)(300,383)(301,382)(302,381)(303,380)(304,379)(305,378)(306,377)(307,376)(308,375)(309,374)(310,373)(311,372)(312,371)(313,370)(314,369)(315,368)(316,367)(317,366)(318,365)(319,364)(320,363)(321,362)(322,361)(323,360)(324,359)(325,358)(326,357)(327,356)(328,355)(329,354)(330,353)(331,352)(332,351)(333,350)(334,349)(335,348)(336,347)(337,346)(338,345)(339,344)(340,343)(341,342)
Conjugacy classes & character table
5934 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23724, 8);
Finite Group Databasebeta