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Dic2705 #24925259
Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 550 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);(1,3,2,4)(6,9)(7,8)(11,550)(12,549)(13,548)(14,547)(15,546)(16,545)(17,544)(18,543)(19,542)(20,541)(21,540)(22,539)(23,538)(24,537)(25,536)(26,535)(27,534)(28,533)(29,532)(30,531)(31,530)(32,529)(33,528)(34,527)(35,526)(36,525)(37,524)(38,523)(39,522)(40,521)(41,520)(42,519)(43,518)(44,517)(45,516)(46,515)(47,514)(48,513)(49,512)(50,511)(51,510)(52,509)(53,508)(54,507)(55,506)(56,505)(57,504)(58,503)(59,502)(60,501)(61,500)(62,499)(63,498)(64,497)(65,496)(66,495)(67,494)(68,493)(69,492)(70,491)(71,490)(72,489)(73,488)(74,487)(75,486)(76,485)(77,484)(78,483)(79,482)(80,481)(81,480)(82,479)(83,478)(84,477)(85,476)(86,475)(87,474)(88,473)(89,472)(90,471)(91,470)(92,469)(93,468)(94,467)(95,466)(96,465)(97,464)(98,463)(99,462)(100,461)(101,460)(102,459)(103,458)(104,457)(105,456)(106,455)(107,454)(108,453)(109,452)(110,451)(111,450)(112,449)(113,448)(114,447)(115,446)(116,445)(117,444)(118,443)(119,442)(120,441)(121,440)(122,439)(123,438)(124,437)(125,436)(126,435)(127,434)(128,433)(129,432)(130,431)(131,430)(132,429)(133,428)(134,427)(135,426)(136,425)(137,424)(138,423)(139,422)(140,421)(141,420)(142,419)(143,418)(144,417)(145,416)(146,415)(147,414)(148,413)(149,412)(150,411)(151,410)(152,409)(153,408)(154,407)(155,406)(156,405)(157,404)(158,403)(159,402)(160,401)(161,400)(162,399)(163,398)(164,397)(165,396)(166,395)(167,394)(168,393)(169,392)(170,391)(171,390)(172,389)(173,388)(174,387)(175,386)(176,385)(177,384)(178,383)(179,382)(180,381)(181,380)(182,379)(183,378)(184,377)(185,376)(186,375)(187,374)(188,373)(189,372)(190,371)(191,370)(192,369)(193,368)(194,367)(195,366)(196,365)(197,364)(198,363)(199,362)(200,361)(201,360)(202,359)(203,358)(204,357)(205,356)(206,355)(207,354)(208,353)(209,352)(210,351)(211,350)(212,349)(213,348)(214,347)(215,346)(216,345)(217,344)(218,343)(219,342)(220,341)(221,340)(222,339)(223,338)(224,337)(225,336)(226,335)(227,334)(228,333)(229,332)(230,331)(231,330)(232,329)(233,328)(234,327)(235,326)(236,325)(237,324)(238,323)(239,322)(240,321)(241,320)(242,319)(243,318)(244,317)(245,316)(246,315)(247,314)(248,313)(249,312)(250,311)(251,310)(252,309)(253,308)(254,307)(255,306)(256,305)(257,304)(258,303)(259,302)(260,301)(261,300)(262,299)(263,298)(264,297)(265,296)(266,295)(267,294)(268,293)(269,292)(270,291)(271,290)(272,289)(273,288)(274,287)(275,286)(276,285)(277,284)(278,283)(279,282)(280,281)
Polycyclic presentation:
2,5,541,2|a^2=d,b^a=b^4,c^a=c^540
Conjugacy classes & character table
2708 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10820, 6);
Finite Group Databasebeta