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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 468 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)(235,315,279,278)(239,320,283,282)(243,316,287,286)(247,312,291,290)(251,309,295,294)(255,305,299,298)(259,301,303,302)(263,297,307,306)(267,293,310,280)(271,289,314,313)(275,285,318,317)(277,281,319,321)(284,350,323,322)(288,352,326,325)(292,351,329,328)(296,349,332,331)(300,346,336,335)(304,342,340,339)(308,338,344,343)(311,334,347,324)(327,377,354,353)(330,379,357,356)(333,378,360,359)(337,376,363,362)(341,373,367,366)(345,369,371,370)(348,365,374,355)(358,400,381,380)(361,402,384,383)(364,401,387,386)(368,399,390,389)(372,396,394,393)(375,392,397,382)(385,419,404,403)(388,421,407,406)(391,420,410,409)(395,418,413,412)(398,415,416,405)(408,434,423,422)(411,436,426,425)(414,435,429,428)(417,433,431,424)(427,445,438,437)(430,447,441,440)(432,446,443,439)(442,453,449,448)(444,454,451,450)(452,457,456,455)(458,459,460,461,462,463,464,465,466,467,468);(1,2,5,10,19,32,49,70,95,124,157,194,235,280,261,216,175,138,105,76,51,30,46,65,86,111,140,173,210,251,296,333,361,385,405,393,366,335,294,245,200,159,122,154,189,226,267,311,348,375,398,417,432,444,452,455,448,437,422,403,380,353,322,278,314,270,229,190,227,268,312,349,376,399,418,433,423,407,387,363,336,299,254,213,176,143,114,89,66,87,112,141,174,211,252,297,334,323,283,238,197,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,195,236,281,313,265,220,179,142,109,80,55,34,17,29,44,61,82,107,136,169,206,247,292,330,358,382,370,339,298,249,204,163,126,93,121,152,185,222,263,308,345,372,395,414,430,442,450,440,425,406,383,356,325,282,233,277,318,274,231,272,316,351,378,401,420,435,446,438,426,410,390,367,340,303,258,217,180,147,118,91,116,145,178,215,256,301,338,365,354,326,287,242,201,164,131,102,77,56,39,26,15,24,37,54,75,100,129,162,199,240,285,317,269,224,183,146,113,84,59,38,21,8,16,27,40,57,78,103,132,165,202,243,288,327,355,343,302,253,208,167,130,97,68,92,119,148,181,218,259,304,341,368,391,411,427,439,428,409,386,359,328,286,237,192,232,275,319,276,320,352,379,402,421,436,447,454,449,441,429,413,394,371,344,307,262,221,184,151,120,149,182,219,260,305,342,369,392,381,357,329,291,246,205,168,135,106,81,60,43,28,41,58,79,104,133,166,203,244,289,321,273,228,187,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,161,198,239,284,324,306,257,212,171,134,101,72,47,67,90,115,144,177,214,255,300,337,364,388,408,424,412,389,362,331,290,241,196,155,191,230,271,315,350,377,400,419,434,445,453,457,456,451,443,431,416,397,374,347,310,266,225,188,153,186,223,264,309,346,373,396,415,404,384,360,332,295,250,209,172,139,110,85,64,45,62,83,108,137,170,207,248,293,279,234,193,156,123,94,69,48,31,18,9,4)
Conjugacy classes & character table
1298 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20108, 6);
Finite Group Databasebeta