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Dic5877 #37555079
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 666 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,666)(16,665)(17,664)(18,663)(19,662)(20,661)(21,660)(22,659)(23,658)(24,657)(25,656)(26,655)(27,654)(28,653)(29,652)(30,651)(31,650)(32,649)(33,648)(34,647)(35,646)(36,645)(37,644)(38,643)(39,642)(40,641)(41,640)(42,639)(43,638)(44,637)(45,636)(46,635)(47,634)(48,633)(49,632)(50,631)(51,630)(52,629)(53,628)(54,627)(55,626)(56,625)(57,624)(58,623)(59,622)(60,621)(61,620)(62,619)(63,618)(64,617)(65,616)(66,615)(67,614)(68,613)(69,612)(70,611)(71,610)(72,609)(73,608)(74,607)(75,606)(76,605)(77,604)(78,603)(79,602)(80,601)(81,600)(82,599)(83,598)(84,597)(85,596)(86,595)(87,594)(88,593)(89,592)(90,591)(91,590)(92,589)(93,588)(94,587)(95,586)(96,585)(97,584)(98,583)(99,582)(100,581)(101,580)(102,579)(103,578)(104,577)(105,576)(106,575)(107,574)(108,573)(109,572)(110,571)(111,570)(112,569)(113,568)(114,567)(115,566)(116,565)(117,564)(118,563)(119,562)(120,561)(121,560)(122,559)(123,558)(124,557)(125,556)(126,555)(127,554)(128,553)(129,552)(130,551)(131,550)(132,549)(133,548)(134,547)(135,546)(136,545)(137,544)(138,543)(139,542)(140,541)(141,540)(142,539)(143,538)(144,537)(145,536)(146,535)(147,534)(148,533)(149,532)(150,531)(151,530)(152,529)(153,528)(154,527)(155,526)(156,525)(157,524)(158,523)(159,522)(160,521)(161,520)(162,519)(163,518)(164,517)(165,516)(166,515)(167,514)(168,513)(169,512)(170,511)(171,510)(172,509)(173,508)(174,507)(175,506)(176,505)(177,504)(178,503)(179,502)(180,501)(181,500)(182,499)(183,498)(184,497)(185,496)(186,495)(187,494)(188,493)(189,492)(190,491)(191,490)(192,489)(193,488)(194,487)(195,486)(196,485)(197,484)(198,483)(199,482)(200,481)(201,480)(202,479)(203,478)(204,477)(205,476)(206,475)(207,474)(208,473)(209,472)(210,471)(211,470)(212,469)(213,468)(214,467)(215,466)(216,465)(217,464)(218,463)(219,462)(220,461)(221,460)(222,459)(223,458)(224,457)(225,456)(226,455)(227,454)(228,453)(229,452)(230,451)(231,450)(232,449)(233,448)(234,447)(235,446)(236,445)(237,444)(238,443)(239,442)(240,441)(241,440)(242,439)(243,438)(244,437)(245,436)(246,435)(247,434)(248,433)(249,432)(250,431)(251,430)(252,429)(253,428)(254,427)(255,426)(256,425)(257,424)(258,423)(259,422)(260,421)(261,420)(262,419)(263,418)(264,417)(265,416)(266,415)(267,414)(268,413)(269,412)(270,411)(271,410)(272,409)(273,408)(274,407)(275,406)(276,405)(277,404)(278,403)(279,402)(280,401)(281,400)(282,399)(283,398)(284,397)(285,396)(286,395)(287,394)(288,393)(289,392)(290,391)(291,390)(292,389)(293,388)(294,387)(295,386)(296,385)(297,384)(298,383)(299,382)(300,381)(301,380)(302,379)(303,378)(304,377)(305,376)(306,375)(307,374)(308,373)(309,372)(310,371)(311,370)(312,369)(313,368)(314,367)(315,366)(316,365)(317,364)(318,363)(319,362)(320,361)(321,360)(322,359)(323,358)(324,357)(325,356)(326,355)(327,354)(328,353)(329,352)(330,351)(331,350)(332,349)(333,348)(334,347)(335,346)(336,345)(337,344)(338,343)(339,342)(340,341)
Polycyclic presentation:
2,3,653,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^652,e^a=e^2
Conjugacy classes & character table
5880 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23508, 4);
Finite Group Databasebeta