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Dic7051 #43245689
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 656 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,656)(18,655)(19,654)(20,653)(21,652)(22,651)(23,650)(24,649)(25,648)(26,647)(27,646)(28,645)(29,644)(30,643)(31,642)(32,641)(33,640)(34,639)(35,638)(36,637)(37,636)(38,635)(39,634)(40,633)(41,632)(42,631)(43,630)(44,629)(45,628)(46,627)(47,626)(48,625)(49,624)(50,623)(51,622)(52,621)(53,620)(54,619)(55,618)(56,617)(57,616)(58,615)(59,614)(60,613)(61,612)(62,611)(63,610)(64,609)(65,608)(66,607)(67,606)(68,605)(69,604)(70,603)(71,602)(72,601)(73,600)(74,599)(75,598)(76,597)(77,596)(78,595)(79,594)(80,593)(81,592)(82,591)(83,590)(84,589)(85,588)(86,587)(87,586)(88,585)(89,584)(90,583)(91,582)(92,581)(93,580)(94,579)(95,578)(96,577)(97,576)(98,575)(99,574)(100,573)(101,572)(102,571)(103,570)(104,569)(105,568)(106,567)(107,566)(108,565)(109,564)(110,563)(111,562)(112,561)(113,560)(114,559)(115,558)(116,557)(117,556)(118,555)(119,554)(120,553)(121,552)(122,551)(123,550)(124,549)(125,548)(126,547)(127,546)(128,545)(129,544)(130,543)(131,542)(132,541)(133,540)(134,539)(135,538)(136,537)(137,536)(138,535)(139,534)(140,533)(141,532)(142,531)(143,530)(144,529)(145,528)(146,527)(147,526)(148,525)(149,524)(150,523)(151,522)(152,521)(153,520)(154,519)(155,518)(156,517)(157,516)(158,515)(159,514)(160,513)(161,512)(162,511)(163,510)(164,509)(165,508)(166,507)(167,506)(168,505)(169,504)(170,503)(171,502)(172,501)(173,500)(174,499)(175,498)(176,497)(177,496)(178,495)(179,494)(180,493)(181,492)(182,491)(183,490)(184,489)(185,488)(186,487)(187,486)(188,485)(189,484)(190,483)(191,482)(192,481)(193,480)(194,479)(195,478)(196,477)(197,476)(198,475)(199,474)(200,473)(201,472)(202,471)(203,470)(204,469)(205,468)(206,467)(207,466)(208,465)(209,464)(210,463)(211,462)(212,461)(213,460)(214,459)(215,458)(216,457)(217,456)(218,455)(219,454)(220,453)(221,452)(222,451)(223,450)(224,449)(225,448)(226,447)(227,446)(228,445)(229,444)(230,443)(231,442)(232,441)(233,440)(234,439)(235,438)(236,437)(237,436)(238,435)(239,434)(240,433)(241,432)(242,431)(243,430)(244,429)(245,428)(246,427)(247,426)(248,425)(249,424)(250,423)(251,422)(252,421)(253,420)(254,419)(255,418)(256,417)(257,416)(258,415)(259,414)(260,413)(261,412)(262,411)(263,410)(264,409)(265,408)(266,407)(267,406)(268,405)(269,404)(270,403)(271,402)(272,401)(273,400)(274,399)(275,398)(276,397)(277,396)(278,395)(279,394)(280,393)(281,392)(282,391)(283,390)(284,389)(285,388)(286,387)(287,386)(288,385)(289,384)(290,383)(291,382)(292,381)(293,380)(294,379)(295,378)(296,377)(297,376)(298,375)(299,374)(300,373)(301,372)(302,371)(303,370)(304,369)(305,368)(306,367)(307,366)(308,365)(309,364)(310,363)(311,362)(312,361)(313,360)(314,359)(315,358)(316,357)(317,356)(318,355)(319,354)(320,353)(321,352)(322,351)(323,350)(324,349)(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)(331,342)(332,341)(333,340)(334,339)(335,338)(336,337)
Polycyclic presentation:
2,11,641,2|a^2=d,b^a=b^10,c^a=c^640
Conjugacy classes & character table
7054 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28204, 4);
Finite Group Databasebeta