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Dic5769 #37528063
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 654 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,654)(16,653)(17,652)(18,651)(19,650)(20,649)(21,648)(22,647)(23,646)(24,645)(25,644)(26,643)(27,642)(28,641)(29,640)(30,639)(31,638)(32,637)(33,636)(34,635)(35,634)(36,633)(37,632)(38,631)(39,630)(40,629)(41,628)(42,627)(43,626)(44,625)(45,624)(46,623)(47,622)(48,621)(49,620)(50,619)(51,618)(52,617)(53,616)(54,615)(55,614)(56,613)(57,612)(58,611)(59,610)(60,609)(61,608)(62,607)(63,606)(64,605)(65,604)(66,603)(67,602)(68,601)(69,600)(70,599)(71,598)(72,597)(73,596)(74,595)(75,594)(76,593)(77,592)(78,591)(79,590)(80,589)(81,588)(82,587)(83,586)(84,585)(85,584)(86,583)(87,582)(88,581)(89,580)(90,579)(91,578)(92,577)(93,576)(94,575)(95,574)(96,573)(97,572)(98,571)(99,570)(100,569)(101,568)(102,567)(103,566)(104,565)(105,564)(106,563)(107,562)(108,561)(109,560)(110,559)(111,558)(112,557)(113,556)(114,555)(115,554)(116,553)(117,552)(118,551)(119,550)(120,549)(121,548)(122,547)(123,546)(124,545)(125,544)(126,543)(127,542)(128,541)(129,540)(130,539)(131,538)(132,537)(133,536)(134,535)(135,534)(136,533)(137,532)(138,531)(139,530)(140,529)(141,528)(142,527)(143,526)(144,525)(145,524)(146,523)(147,522)(148,521)(149,520)(150,519)(151,518)(152,517)(153,516)(154,515)(155,514)(156,513)(157,512)(158,511)(159,510)(160,509)(161,508)(162,507)(163,506)(164,505)(165,504)(166,503)(167,502)(168,501)(169,500)(170,499)(171,498)(172,497)(173,496)(174,495)(175,494)(176,493)(177,492)(178,491)(179,490)(180,489)(181,488)(182,487)(183,486)(184,485)(185,484)(186,483)(187,482)(188,481)(189,480)(190,479)(191,478)(192,477)(193,476)(194,475)(195,474)(196,473)(197,472)(198,471)(199,470)(200,469)(201,468)(202,467)(203,466)(204,465)(205,464)(206,463)(207,462)(208,461)(209,460)(210,459)(211,458)(212,457)(213,456)(214,455)(215,454)(216,453)(217,452)(218,451)(219,450)(220,449)(221,448)(222,447)(223,446)(224,445)(225,444)(226,443)(227,442)(228,441)(229,440)(230,439)(231,438)(232,437)(233,436)(234,435)(235,434)(236,433)(237,432)(238,431)(239,430)(240,429)(241,428)(242,427)(243,426)(244,425)(245,424)(246,423)(247,422)(248,421)(249,420)(250,419)(251,418)(252,417)(253,416)(254,415)(255,414)(256,413)(257,412)(258,411)(259,410)(260,409)(261,408)(262,407)(263,406)(264,405)(265,404)(266,403)(267,402)(268,401)(269,400)(270,399)(271,398)(272,397)(273,396)(274,395)(275,394)(276,393)(277,392)(278,391)(279,390)(280,389)(281,388)(282,387)(283,386)(284,385)(285,384)(286,383)(287,382)(288,381)(289,380)(290,379)(291,378)(292,377)(293,376)(294,375)(295,374)(296,373)(297,372)(298,371)(299,370)(300,369)(301,368)(302,367)(303,366)(304,365)(305,364)(306,363)(307,362)(308,361)(309,360)(310,359)(311,358)(312,357)(313,356)(314,355)(315,354)(316,353)(317,352)(318,351)(319,350)(320,349)(321,348)(322,347)(323,346)(324,345)(325,344)(326,343)(327,342)(328,341)(329,340)(330,339)(331,338)(332,337)(333,336)(334,335)
Polycyclic presentation:
2,3,641,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^640,e^a=e^2
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, 4);
Finite Group Databasebeta