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Dic6383 #38784302
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 508 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);(1,3,2,4)(6,17)(7,16)(8,15)(9,14)(10,13)(11,12)(19,508)(20,507)(21,506)(22,505)(23,504)(24,503)(25,502)(26,501)(27,500)(28,499)(29,498)(30,497)(31,496)(32,495)(33,494)(34,493)(35,492)(36,491)(37,490)(38,489)(39,488)(40,487)(41,486)(42,485)(43,484)(44,483)(45,482)(46,481)(47,480)(48,479)(49,478)(50,477)(51,476)(52,475)(53,474)(54,473)(55,472)(56,471)(57,470)(58,469)(59,468)(60,467)(61,466)(62,465)(63,464)(64,463)(65,462)(66,461)(67,460)(68,459)(69,458)(70,457)(71,456)(72,455)(73,454)(74,453)(75,452)(76,451)(77,450)(78,449)(79,448)(80,447)(81,446)(82,445)(83,444)(84,443)(85,442)(86,441)(87,440)(88,439)(89,438)(90,437)(91,436)(92,435)(93,434)(94,433)(95,432)(96,431)(97,430)(98,429)(99,428)(100,427)(101,426)(102,425)(103,424)(104,423)(105,422)(106,421)(107,420)(108,419)(109,418)(110,417)(111,416)(112,415)(113,414)(114,413)(115,412)(116,411)(117,410)(118,409)(119,408)(120,407)(121,406)(122,405)(123,404)(124,403)(125,402)(126,401)(127,400)(128,399)(129,398)(130,397)(131,396)(132,395)(133,394)(134,393)(135,392)(136,391)(137,390)(138,389)(139,388)(140,387)(141,386)(142,385)(143,384)(144,383)(145,382)(146,381)(147,380)(148,379)(149,378)(150,377)(151,376)(152,375)(153,374)(154,373)(155,372)(156,371)(157,370)(158,369)(159,368)(160,367)(161,366)(162,365)(163,364)(164,363)(165,362)(166,361)(167,360)(168,359)(169,358)(170,357)(171,356)(172,355)(173,354)(174,353)(175,352)(176,351)(177,350)(178,349)(179,348)(180,347)(181,346)(182,345)(183,344)(184,343)(185,342)(186,341)(187,340)(188,339)(189,338)(190,337)(191,336)(192,335)(193,334)(194,333)(195,332)(196,331)(197,330)(198,329)(199,328)(200,327)(201,326)(202,325)(203,324)(204,323)(205,322)(206,321)(207,320)(208,319)(209,318)(210,317)(211,316)(212,315)(213,314)(214,313)(215,312)(216,311)(217,310)(218,309)(219,308)(220,307)(221,306)(222,305)(223,304)(224,303)(225,302)(226,301)(227,300)(228,299)(229,298)(230,297)(231,296)(232,295)(233,294)(234,293)(235,292)(236,291)(237,290)(238,289)(239,288)(240,287)(241,286)(242,285)(243,284)(244,283)(245,282)(246,281)(247,280)(248,279)(249,278)(250,277)(251,276)(252,275)(253,274)(254,273)(255,272)(256,271)(257,270)(258,269)(259,268)(260,267)(261,266)(262,265)(263,264)
Polycyclic presentation:
2,13,491,2|a^2=d,b^a=b^12,c^a=c^490
Conjugacy classes & character table
6386 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25532, 4);
Finite Group Databasebeta