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Dic4627 #32915025
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 672 points:
(1,2)(3,4)(5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672);(1,3,2,4)(6,11)(7,10)(8,9)(13,672)(14,671)(15,670)(16,669)(17,668)(18,667)(19,666)(20,665)(21,664)(22,663)(23,662)(24,661)(25,660)(26,659)(27,658)(28,657)(29,656)(30,655)(31,654)(32,653)(33,652)(34,651)(35,650)(36,649)(37,648)(38,647)(39,646)(40,645)(41,644)(42,643)(43,642)(44,641)(45,640)(46,639)(47,638)(48,637)(49,636)(50,635)(51,634)(52,633)(53,632)(54,631)(55,630)(56,629)(57,628)(58,627)(59,626)(60,625)(61,624)(62,623)(63,622)(64,621)(65,620)(66,619)(67,618)(68,617)(69,616)(70,615)(71,614)(72,613)(73,612)(74,611)(75,610)(76,609)(77,608)(78,607)(79,606)(80,605)(81,604)(82,603)(83,602)(84,601)(85,600)(86,599)(87,598)(88,597)(89,596)(90,595)(91,594)(92,593)(93,592)(94,591)(95,590)(96,589)(97,588)(98,587)(99,586)(100,585)(101,584)(102,583)(103,582)(104,581)(105,580)(106,579)(107,578)(108,577)(109,576)(110,575)(111,574)(112,573)(113,572)(114,571)(115,570)(116,569)(117,568)(118,567)(119,566)(120,565)(121,564)(122,563)(123,562)(124,561)(125,560)(126,559)(127,558)(128,557)(129,556)(130,555)(131,554)(132,553)(133,552)(134,551)(135,550)(136,549)(137,548)(138,547)(139,546)(140,545)(141,544)(142,543)(143,542)(144,541)(145,540)(146,539)(147,538)(148,537)(149,536)(150,535)(151,534)(152,533)(153,532)(154,531)(155,530)(156,529)(157,528)(158,527)(159,526)(160,525)(161,524)(162,523)(163,522)(164,521)(165,520)(166,519)(167,518)(168,517)(169,516)(170,515)(171,514)(172,513)(173,512)(174,511)(175,510)(176,509)(177,508)(178,507)(179,506)(180,505)(181,504)(182,503)(183,502)(184,501)(185,500)(186,499)(187,498)(188,497)(189,496)(190,495)(191,494)(192,493)(193,492)(194,491)(195,490)(196,489)(197,488)(198,487)(199,486)(200,485)(201,484)(202,483)(203,482)(204,481)(205,480)(206,479)(207,478)(208,477)(209,476)(210,475)(211,474)(212,473)(213,472)(214,471)(215,470)(216,469)(217,468)(218,467)(219,466)(220,465)(221,464)(222,463)(223,462)(224,461)(225,460)(226,459)(227,458)(228,457)(229,456)(230,455)(231,454)(232,453)(233,452)(234,451)(235,450)(236,449)(237,448)(238,447)(239,446)(240,445)(241,444)(242,443)(243,442)(244,441)(245,440)(246,439)(247,438)(248,437)(249,436)(250,435)(251,434)(252,433)(253,432)(254,431)(255,430)(256,429)(257,428)(258,427)(259,426)(260,425)(261,424)(262,423)(263,422)(264,421)(265,420)(266,419)(267,418)(268,417)(269,416)(270,415)(271,414)(272,413)(273,412)(274,411)(275,410)(276,409)(277,408)(278,407)(279,406)(280,405)(281,404)(282,403)(283,402)(284,401)(285,400)(286,399)(287,398)(288,397)(289,396)(290,395)(291,394)(292,393)(293,392)(294,391)(295,390)(296,389)(297,388)(298,387)(299,386)(300,385)(301,384)(302,383)(303,382)(304,381)(305,380)(306,379)(307,378)(308,377)(309,376)(310,375)(311,374)(312,373)(313,372)(314,371)(315,370)(316,369)(317,368)(318,367)(319,366)(320,365)(321,364)(322,363)(323,362)(324,361)(325,360)(326,359)(327,358)(328,357)(329,356)(330,355)(331,354)(332,353)(333,352)(334,351)(335,350)(336,349)(337,348)(338,347)(339,346)(340,345)(341,344)(342,343)
Polycyclic presentation:
2,7,661,2|a^2=d,b^a=b^6,c^a=c^660
Conjugacy classes & character table
4630 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18508, 4);
Finite Group Databasebeta