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D1671 #16809757
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 560 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);(2,3)(5,560)(6,559)(7,558)(8,557)(9,556)(10,555)(11,554)(12,553)(13,552)(14,551)(15,550)(16,549)(17,548)(18,547)(19,546)(20,545)(21,544)(22,543)(23,542)(24,541)(25,540)(26,539)(27,538)(28,537)(29,536)(30,535)(31,534)(32,533)(33,532)(34,531)(35,530)(36,529)(37,528)(38,527)(39,526)(40,525)(41,524)(42,523)(43,522)(44,521)(45,520)(46,519)(47,518)(48,517)(49,516)(50,515)(51,514)(52,513)(53,512)(54,511)(55,510)(56,509)(57,508)(58,507)(59,506)(60,505)(61,504)(62,503)(63,502)(64,501)(65,500)(66,499)(67,498)(68,497)(69,496)(70,495)(71,494)(72,493)(73,492)(74,491)(75,490)(76,489)(77,488)(78,487)(79,486)(80,485)(81,484)(82,483)(83,482)(84,481)(85,480)(86,479)(87,478)(88,477)(89,476)(90,475)(91,474)(92,473)(93,472)(94,471)(95,470)(96,469)(97,468)(98,467)(99,466)(100,465)(101,464)(102,463)(103,462)(104,461)(105,460)(106,459)(107,458)(108,457)(109,456)(110,455)(111,454)(112,453)(113,452)(114,451)(115,450)(116,449)(117,448)(118,447)(119,446)(120,445)(121,444)(122,443)(123,442)(124,441)(125,440)(126,439)(127,438)(128,437)(129,436)(130,435)(131,434)(132,433)(133,432)(134,431)(135,430)(136,429)(137,428)(138,427)(139,426)(140,425)(141,424)(142,423)(143,422)(144,421)(145,420)(146,419)(147,418)(148,417)(149,416)(150,415)(151,414)(152,413)(153,412)(154,411)(155,410)(156,409)(157,408)(158,407)(159,406)(160,405)(161,404)(162,403)(163,402)(164,401)(165,400)(166,399)(167,398)(168,397)(169,396)(170,395)(171,394)(172,393)(173,392)(174,391)(175,390)(176,389)(177,388)(178,387)(179,386)(180,385)(181,384)(182,383)(183,382)(184,381)(185,380)(186,379)(187,378)(188,377)(189,376)(190,375)(191,374)(192,373)(193,372)(194,371)(195,370)(196,369)(197,368)(198,367)(199,366)(200,365)(201,364)(202,363)(203,362)(204,361)(205,360)(206,359)(207,358)(208,357)(209,356)(210,355)(211,354)(212,353)(213,352)(214,351)(215,350)(216,349)(217,348)(218,347)(219,346)(220,345)(221,344)(222,343)(223,342)(224,341)(225,340)(226,339)(227,338)(228,337)(229,336)(230,335)(231,334)(232,333)(233,332)(234,331)(235,330)(236,329)(237,328)(238,327)(239,326)(240,325)(241,324)(242,323)(243,322)(244,321)(245,320)(246,319)(247,318)(248,317)(249,316)(250,315)(251,314)(252,313)(253,312)(254,311)(255,310)(256,309)(257,308)(258,307)(259,306)(260,305)(261,304)(262,303)(263,302)(264,301)(265,300)(266,299)(267,298)(268,297)(269,296)(270,295)(271,294)(272,293)(273,292)(274,291)(275,290)(276,289)(277,288)(278,287)(279,286)(280,285)(281,284)(282,283)
Polycyclic presentation:
2,3,557|b^a=b^2,c^a=c^556
Conjugacy classes & character table
837 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3342, 3);
Finite Group Databasebeta