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Aliases
Splittings
Subgroups
36 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 563 points:
(2,6,4,3)(5,15,9,8)(7,11,13,12)(10,28,18,17)(14,24,22,21)(16,20,26,25)(19,45,31,30)(23,41,35,34)(27,37,39,38)(29,33,43,42)(32,66,48,47)(36,62,52,51)(40,58,56,55)(44,54,60,59)(46,50,64,63)(49,91,69,68)(53,87,73,72)(57,83,77,76)(61,79,81,80)(65,75,85,84)(67,71,89,88)(70,120,94,93)(74,116,98,97)(78,112,102,101)(82,108,106,105)(86,104,110,109)(90,100,114,113)(92,96,118,117)(95,153,123,122)(99,149,127,126)(103,145,131,130)(107,141,135,134)(111,137,139,138)(115,133,143,142)(119,129,147,146)(121,125,151,150)(124,190,156,155)(128,186,160,159)(132,182,164,163)(136,178,168,167)(140,174,172,171)(144,170,176,175)(148,166,180,179)(152,162,184,183)(154,158,188,187)(157,231,193,192)(161,227,197,196)(165,223,201,200)(169,219,205,204)(173,215,209,208)(177,211,213,212)(181,207,217,216)(185,203,221,220)(189,199,225,224)(191,195,229,228)(194,276,234,233)(198,272,238,237)(202,268,242,241)(206,264,246,245)(210,260,250,249)(214,256,254,253)(218,252,258,257)(222,248,262,261)(226,244,266,265)(230,240,270,269)(232,236,274,273)(235,325,279,278)(239,321,283,282)(243,317,287,286)(247,313,291,290)(251,309,295,294)(255,305,299,298)(259,301,303,302)(263,297,307,306)(267,293,311,310)(271,289,315,314)(275,285,319,318)(277,281,323,322)(280,378,328,327)(284,374,332,331)(288,370,336,335)(292,366,340,339)(296,362,344,343)(300,358,348,347)(304,354,352,351)(308,350,356,355)(312,346,360,359)(316,342,364,363)(320,338,368,367)(324,334,372,371)(326,330,376,375)(329,435,381,380)(333,431,385,384)(337,427,389,388)(341,423,393,392)(345,419,397,396)(349,415,401,400)(353,411,405,404)(357,407,409,408)(361,403,413,412)(365,399,417,416)(369,395,421,420)(373,391,425,424)(377,387,429,428)(379,383,433,432)(382,496,438,437)(386,492,442,441)(390,488,446,445)(394,484,450,449)(398,480,454,453)(402,476,458,457)(406,472,462,461)(410,468,466,465)(414,464,470,469)(418,460,474,473)(422,456,478,477)(426,452,482,481)(430,448,486,485)(434,444,490,489)(436,440,494,493)(439,546,499,498)(443,542,503,502)(447,540,507,506)(451,538,511,510)(455,536,515,514)(459,534,519,518)(463,532,523,522)(467,530,527,526)(471,528,524,529)(475,525,520,531)(479,521,516,533)(483,517,512,535)(487,513,508,537)(491,509,504,539)(495,505,500,541)(497,501,544,543)(545,549,551,550)(547,548,553,552)(554,555,557,556)(561,562,563);(1,2,5,10,19,32,49,70,95,124,157,194,235,280,329,382,439,500,494,435,492,540,535,477,416,359,306,257,212,171,134,101,72,47,67,90,115,144,177,214,255,300,349,402,459,520,474,417,364,315,270,229,190,227,268,313,362,415,472,530,522,457,396,339,286,237,192,232,275,320,369,422,479,515,454,397,344,295,250,209,172,139,110,85,64,45,62,83,108,137,170,207,248,293,342,395,452,513,502,437,497,545,552,543,493,432,375,322,273,228,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,239,284,333,386,443,504,490,433,378,431,488,538,533,473,412,355,302,253,208,167,130,97,68,92,119,148,181,218,259,304,353,406,463,524,470,413,360,311,266,225,188,153,186,223,264,309,358,411,468,528,518,453,392,335,282,233,277,324,373,426,483,511,450,393,340,291,246,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,244,289,338,391,448,509,498,547,554,556,550,541,489,428,371,318,269,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,243,288,337,390,447,508,486,429,376,325,374,427,484,536,531,469,408,351,298,249,204,163,126,93,121,152,185,222,263,308,357,410,467,527,466,409,356,307,262,221,184,151,120,149,182,219,260,305,354,407,464,525,514,449,388,331,278,326,377,430,487,507,446,389,336,287,242,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,240,285,334,387,444,505,549,555,557,553,546,539,485,424,367,314,265,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,247,292,341,394,451,512,482,425,372,323,276,321,370,423,480,534,529,465,404,347,294,245,200,159,122,154,189,226,267,312,361,414,471,523,462,405,352,303,258,217,180,147,118,91,116,145,178,215,256,301,350,403,460,521,510,445,384,327,379,434,491,503,442,385,332,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,330,383,440,501,548,551,544,496,542,537,481,420,363,310,261,216,175,138,105,76,51,30,46,65,86,111,140,173,210,251,296,345,398,455,516,478,421,368,319,274,231,272,317,366,419,476,532,526,461,400,343,290,241,196,155,191,230,271,316,365,418,475,519,458,401,348,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,346,399,456,517,506,441,380,436,495,499,438,381,328,279,234,193,156,123,94,69,48,31,18,9,4)(558,559,560)
Conjugacy classes & character table
1287 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20052, 23);
Finite Group Databasebeta