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Dic7117 #43249671
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 662 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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,662)(18,661)(19,660)(20,659)(21,658)(22,657)(23,656)(24,655)(25,654)(26,653)(27,652)(28,651)(29,650)(30,649)(31,648)(32,647)(33,646)(34,645)(35,644)(36,643)(37,642)(38,641)(39,640)(40,639)(41,638)(42,637)(43,636)(44,635)(45,634)(46,633)(47,632)(48,631)(49,630)(50,629)(51,628)(52,627)(53,626)(54,625)(55,624)(56,623)(57,622)(58,621)(59,620)(60,619)(61,618)(62,617)(63,616)(64,615)(65,614)(66,613)(67,612)(68,611)(69,610)(70,609)(71,608)(72,607)(73,606)(74,605)(75,604)(76,603)(77,602)(78,601)(79,600)(80,599)(81,598)(82,597)(83,596)(84,595)(85,594)(86,593)(87,592)(88,591)(89,590)(90,589)(91,588)(92,587)(93,586)(94,585)(95,584)(96,583)(97,582)(98,581)(99,580)(100,579)(101,578)(102,577)(103,576)(104,575)(105,574)(106,573)(107,572)(108,571)(109,570)(110,569)(111,568)(112,567)(113,566)(114,565)(115,564)(116,563)(117,562)(118,561)(119,560)(120,559)(121,558)(122,557)(123,556)(124,555)(125,554)(126,553)(127,552)(128,551)(129,550)(130,549)(131,548)(132,547)(133,546)(134,545)(135,544)(136,543)(137,542)(138,541)(139,540)(140,539)(141,538)(142,537)(143,536)(144,535)(145,534)(146,533)(147,532)(148,531)(149,530)(150,529)(151,528)(152,527)(153,526)(154,525)(155,524)(156,523)(157,522)(158,521)(159,520)(160,519)(161,518)(162,517)(163,516)(164,515)(165,514)(166,513)(167,512)(168,511)(169,510)(170,509)(171,508)(172,507)(173,506)(174,505)(175,504)(176,503)(177,502)(178,501)(179,500)(180,499)(181,498)(182,497)(183,496)(184,495)(185,494)(186,493)(187,492)(188,491)(189,490)(190,489)(191,488)(192,487)(193,486)(194,485)(195,484)(196,483)(197,482)(198,481)(199,480)(200,479)(201,478)(202,477)(203,476)(204,475)(205,474)(206,473)(207,472)(208,471)(209,470)(210,469)(211,468)(212,467)(213,466)(214,465)(215,464)(216,463)(217,462)(218,461)(219,460)(220,459)(221,458)(222,457)(223,456)(224,455)(225,454)(226,453)(227,452)(228,451)(229,450)(230,449)(231,448)(232,447)(233,446)(234,445)(235,444)(236,443)(237,442)(238,441)(239,440)(240,439)(241,438)(242,437)(243,436)(244,435)(245,434)(246,433)(247,432)(248,431)(249,430)(250,429)(251,428)(252,427)(253,426)(254,425)(255,424)(256,423)(257,422)(258,421)(259,420)(260,419)(261,418)(262,417)(263,416)(264,415)(265,414)(266,413)(267,412)(268,411)(269,410)(270,409)(271,408)(272,407)(273,406)(274,405)(275,404)(276,403)(277,402)(278,401)(279,400)(280,399)(281,398)(282,397)(283,396)(284,395)(285,394)(286,393)(287,392)(288,391)(289,390)(290,389)(291,388)(292,387)(293,386)(294,385)(295,384)(296,383)(297,382)(298,381)(299,380)(300,379)(301,378)(302,377)(303,376)(304,375)(305,374)(306,373)(307,372)(308,371)(309,370)(310,369)(311,368)(312,367)(313,366)(314,365)(315,364)(316,363)(317,362)(318,361)(319,360)(320,359)(321,358)(322,357)(323,356)(324,355)(325,354)(326,353)(327,352)(328,351)(329,350)(330,349)(331,348)(332,347)(333,346)(334,345)(335,344)(336,343)(337,342)(338,341)(339,340)
Polycyclic presentation:
2,11,647,2|a^2=d,b^a=b^10,c^a=c^646
Conjugacy classes & character table
7120 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28468, 4);
Finite Group Databasebeta