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D13461 #41002181
Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 651 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);(2,3)(5,10)(6,9)(7,8)(12,651)(13,650)(14,649)(15,648)(16,647)(17,646)(18,645)(19,644)(20,643)(21,642)(22,641)(23,640)(24,639)(25,638)(26,637)(27,636)(28,635)(29,634)(30,633)(31,632)(32,631)(33,630)(34,629)(35,628)(36,627)(37,626)(38,625)(39,624)(40,623)(41,622)(42,621)(43,620)(44,619)(45,618)(46,617)(47,616)(48,615)(49,614)(50,613)(51,612)(52,611)(53,610)(54,609)(55,608)(56,607)(57,606)(58,605)(59,604)(60,603)(61,602)(62,601)(63,600)(64,599)(65,598)(66,597)(67,596)(68,595)(69,594)(70,593)(71,592)(72,591)(73,590)(74,589)(75,588)(76,587)(77,586)(78,585)(79,584)(80,583)(81,582)(82,581)(83,580)(84,579)(85,578)(86,577)(87,576)(88,575)(89,574)(90,573)(91,572)(92,571)(93,570)(94,569)(95,568)(96,567)(97,566)(98,565)(99,564)(100,563)(101,562)(102,561)(103,560)(104,559)(105,558)(106,557)(107,556)(108,555)(109,554)(110,553)(111,552)(112,551)(113,550)(114,549)(115,548)(116,547)(117,546)(118,545)(119,544)(120,543)(121,542)(122,541)(123,540)(124,539)(125,538)(126,537)(127,536)(128,535)(129,534)(130,533)(131,532)(132,531)(133,530)(134,529)(135,528)(136,527)(137,526)(138,525)(139,524)(140,523)(141,522)(142,521)(143,520)(144,519)(145,518)(146,517)(147,516)(148,515)(149,514)(150,513)(151,512)(152,511)(153,510)(154,509)(155,508)(156,507)(157,506)(158,505)(159,504)(160,503)(161,502)(162,501)(163,500)(164,499)(165,498)(166,497)(167,496)(168,495)(169,494)(170,493)(171,492)(172,491)(173,490)(174,489)(175,488)(176,487)(177,486)(178,485)(179,484)(180,483)(181,482)(182,481)(183,480)(184,479)(185,478)(186,477)(187,476)(188,475)(189,474)(190,473)(191,472)(192,471)(193,470)(194,469)(195,468)(196,467)(197,466)(198,465)(199,464)(200,463)(201,462)(202,461)(203,460)(204,459)(205,458)(206,457)(207,456)(208,455)(209,454)(210,453)(211,452)(212,451)(213,450)(214,449)(215,448)(216,447)(217,446)(218,445)(219,444)(220,443)(221,442)(222,441)(223,440)(224,439)(225,438)(226,437)(227,436)(228,435)(229,434)(230,433)(231,432)(232,431)(233,430)(234,429)(235,428)(236,427)(237,426)(238,425)(239,424)(240,423)(241,422)(242,421)(243,420)(244,419)(245,418)(246,417)(247,416)(248,415)(249,414)(250,413)(251,412)(252,411)(253,410)(254,409)(255,408)(256,407)(257,406)(258,405)(259,404)(260,403)(261,402)(262,401)(263,400)(264,399)(265,398)(266,397)(267,396)(268,395)(269,394)(270,393)(271,392)(272,391)(273,390)(274,389)(275,388)(276,387)(277,386)(278,385)(279,384)(280,383)(281,382)(282,381)(283,380)(284,379)(285,378)(286,377)(287,376)(288,375)(289,374)(290,373)(291,372)(292,371)(293,370)(294,369)(295,368)(296,367)(297,366)(298,365)(299,364)(300,363)(301,362)(302,361)(303,360)(304,359)(305,358)(306,357)(307,356)(308,355)(309,354)(310,353)(311,352)(312,351)(313,350)(314,349)(315,348)(316,347)(317,346)(318,345)(319,344)(320,343)(321,342)(322,341)(323,340)(324,339)(325,338)(326,337)(327,336)(328,335)(329,334)(330,333)(331,332)
Polycyclic presentation:
2,3,7,641|b^a=b^2,c^a=c^6,d^a=d^640
Conjugacy classes & character table
6732 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26922, 9);
Finite Group Databasebeta