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Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 652 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);(4,11)(5,10)(6,9)(7,8)(13,652)(14,651)(15,650)(16,649)(17,648)(18,647)(19,646)(20,645)(21,644)(22,643)(23,642)(24,641)(25,640)(26,639)(27,638)(28,637)(29,636)(30,635)(31,634)(32,633)(33,632)(34,631)(35,630)(36,629)(37,628)(38,627)(39,626)(40,625)(41,624)(42,623)(43,622)(44,621)(45,620)(46,619)(47,618)(48,617)(49,616)(50,615)(51,614)(52,613)(53,612)(54,611)(55,610)(56,609)(57,608)(58,607)(59,606)(60,605)(61,604)(62,603)(63,602)(64,601)(65,600)(66,599)(67,598)(68,597)(69,596)(70,595)(71,594)(72,593)(73,592)(74,591)(75,590)(76,589)(77,588)(78,587)(79,586)(80,585)(81,584)(82,583)(83,582)(84,581)(85,580)(86,579)(87,578)(88,577)(89,576)(90,575)(91,574)(92,573)(93,572)(94,571)(95,570)(96,569)(97,568)(98,567)(99,566)(100,565)(101,564)(102,563)(103,562)(104,561)(105,560)(106,559)(107,558)(108,557)(109,556)(110,555)(111,554)(112,553)(113,552)(114,551)(115,550)(116,549)(117,548)(118,547)(119,546)(120,545)(121,544)(122,543)(123,542)(124,541)(125,540)(126,539)(127,538)(128,537)(129,536)(130,535)(131,534)(132,533)(133,532)(134,531)(135,530)(136,529)(137,528)(138,527)(139,526)(140,525)(141,524)(142,523)(143,522)(144,521)(145,520)(146,519)(147,518)(148,517)(149,516)(150,515)(151,514)(152,513)(153,512)(154,511)(155,510)(156,509)(157,508)(158,507)(159,506)(160,505)(161,504)(162,503)(163,502)(164,501)(165,500)(166,499)(167,498)(168,497)(169,496)(170,495)(171,494)(172,493)(173,492)(174,491)(175,490)(176,489)(177,488)(178,487)(179,486)(180,485)(181,484)(182,483)(183,482)(184,481)(185,480)(186,479)(187,478)(188,477)(189,476)(190,475)(191,474)(192,473)(193,472)(194,471)(195,470)(196,469)(197,468)(198,467)(199,466)(200,465)(201,464)(202,463)(203,462)(204,461)(205,460)(206,459)(207,458)(208,457)(209,456)(210,455)(211,454)(212,453)(213,452)(214,451)(215,450)(216,449)(217,448)(218,447)(219,446)(220,445)(221,444)(222,443)(223,442)(224,441)(225,440)(226,439)(227,438)(228,437)(229,436)(230,435)(231,434)(232,433)(233,432)(234,431)(235,430)(236,429)(237,428)(238,427)(239,426)(240,425)(241,424)(242,423)(243,422)(244,421)(245,420)(246,419)(247,418)(248,417)(249,416)(250,415)(251,414)(252,413)(253,412)(254,411)(255,410)(256,409)(257,408)(258,407)(259,406)(260,405)(261,404)(262,403)(263,402)(264,401)(265,400)(266,399)(267,398)(268,397)(269,396)(270,395)(271,394)(272,393)(273,392)(274,391)(275,390)(276,389)(277,388)(278,387)(279,386)(280,385)(281,384)(282,383)(283,382)(284,381)(285,380)(286,379)(287,378)(288,377)(289,376)(290,375)(291,374)(292,373)(293,372)(294,371)(295,370)(296,369)(297,368)(298,367)(299,366)(300,365)(301,364)(302,363)(303,362)(304,361)(305,360)(306,359)(307,358)(308,357)(309,356)(310,355)(311,354)(312,353)(313,352)(314,351)(315,350)(316,349)(317,348)(318,347)(319,346)(320,345)(321,344)(322,343)(323,342)(324,341)(325,340)(326,339)(327,338)(328,337)(329,336)(330,335)(331,334)(332,333)
Conjugacy classes & character table
5772 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23076, 10);
Finite Group Databasebeta