← Prev (#36384254) Next (#36384256) →
Dic5679 #36384255
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 644 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,644)(16,643)(17,642)(18,641)(19,640)(20,639)(21,638)(22,637)(23,636)(24,635)(25,634)(26,633)(27,632)(28,631)(29,630)(30,629)(31,628)(32,627)(33,626)(34,625)(35,624)(36,623)(37,622)(38,621)(39,620)(40,619)(41,618)(42,617)(43,616)(44,615)(45,614)(46,613)(47,612)(48,611)(49,610)(50,609)(51,608)(52,607)(53,606)(54,605)(55,604)(56,603)(57,602)(58,601)(59,600)(60,599)(61,598)(62,597)(63,596)(64,595)(65,594)(66,593)(67,592)(68,591)(69,590)(70,589)(71,588)(72,587)(73,586)(74,585)(75,584)(76,583)(77,582)(78,581)(79,580)(80,579)(81,578)(82,577)(83,576)(84,575)(85,574)(86,573)(87,572)(88,571)(89,570)(90,569)(91,568)(92,567)(93,566)(94,565)(95,564)(96,563)(97,562)(98,561)(99,560)(100,559)(101,558)(102,557)(103,556)(104,555)(105,554)(106,553)(107,552)(108,551)(109,550)(110,549)(111,548)(112,547)(113,546)(114,545)(115,544)(116,543)(117,542)(118,541)(119,540)(120,539)(121,538)(122,537)(123,536)(124,535)(125,534)(126,533)(127,532)(128,531)(129,530)(130,529)(131,528)(132,527)(133,526)(134,525)(135,524)(136,523)(137,522)(138,521)(139,520)(140,519)(141,518)(142,517)(143,516)(144,515)(145,514)(146,513)(147,512)(148,511)(149,510)(150,509)(151,508)(152,507)(153,506)(154,505)(155,504)(156,503)(157,502)(158,501)(159,500)(160,499)(161,498)(162,497)(163,496)(164,495)(165,494)(166,493)(167,492)(168,491)(169,490)(170,489)(171,488)(172,487)(173,486)(174,485)(175,484)(176,483)(177,482)(178,481)(179,480)(180,479)(181,478)(182,477)(183,476)(184,475)(185,474)(186,473)(187,472)(188,471)(189,470)(190,469)(191,468)(192,467)(193,466)(194,465)(195,464)(196,463)(197,462)(198,461)(199,460)(200,459)(201,458)(202,457)(203,456)(204,455)(205,454)(206,453)(207,452)(208,451)(209,450)(210,449)(211,448)(212,447)(213,446)(214,445)(215,444)(216,443)(217,442)(218,441)(219,440)(220,439)(221,438)(222,437)(223,436)(224,435)(225,434)(226,433)(227,432)(228,431)(229,430)(230,429)(231,428)(232,427)(233,426)(234,425)(235,424)(236,423)(237,422)(238,421)(239,420)(240,419)(241,418)(242,417)(243,416)(244,415)(245,414)(246,413)(247,412)(248,411)(249,410)(250,409)(251,408)(252,407)(253,406)(254,405)(255,404)(256,403)(257,402)(258,401)(259,400)(260,399)(261,398)(262,397)(263,396)(264,395)(265,394)(266,393)(267,392)(268,391)(269,390)(270,389)(271,388)(272,387)(273,386)(274,385)(275,384)(276,383)(277,382)(278,381)(279,380)(280,379)(281,378)(282,377)(283,376)(284,375)(285,374)(286,373)(287,372)(288,371)(289,370)(290,369)(291,368)(292,367)(293,366)(294,365)(295,364)(296,363)(297,362)(298,361)(299,360)(300,359)(301,358)(302,357)(303,356)(304,355)(305,354)(306,353)(307,352)(308,351)(309,350)(310,349)(311,348)(312,347)(313,346)(314,345)(315,344)(316,343)(317,342)(318,341)(319,340)(320,339)(321,338)(322,337)(323,336)(324,335)(325,334)(326,333)(327,332)(328,331)(329,330)
Polycyclic presentation:
2,3,631,2,3|a^2=d,b^3=e^2,b^a=b^2e,c^a=c^630,e^a=e^2
Conjugacy classes & character table
5682 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22716, 6);
Finite Group Databasebeta