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Aliases
Splittings
Subgroups
44 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 405 points:
(2,3,4,7,5,8,10,16)(6,12,13,28,14,29,31,63)(9,19,20,45,21,46,48,37)(11,24,25,56,26,57,23,54)(15,33,34,75,35,76,78,154)(17,38,39,85,40,18,42,43)(22,50,51,107,52,108,110,132)(27,59,60,125,61,126,70,147)(30,66,67,138,68,139,141,84)(32,71,72,149,73,150,55,117)(36,80,81,166,82,167,169,271)(41,87,88,176,89,65,83,136)(44,93,94,64,95,133,186,134)(47,98,99,191,100,192,102,116)(49,103,104,198,105,120,91,181)(53,112,113,213,114,214,216,277)(58,121,122,183,123,97,189,92)(62,128,129,240,130,241,161,234)(69,143,144,261,145,262,264,243)(74,152,153,275,96,188,148,155)(77,157,158,282,159,278,255,172)(79,162,163,270,164,165,118,224)(86,174,175,119,131,226,173,227)(90,177,178,298,179,156,279,280)(101,194,160,283,195,315,208,269)(106,199,200,263,201,235,171,293)(109,204,205,326,206,260,256,222)(111,209,210,331,211,272,182,304)(115,218,219,334,220,335,336,371)(124,231,146,266,232,203,267,249)(127,236,237,305,238,251,348,184)(135,245,246,215,247,137,221,250)(140,252,253,294,254,212,197,223)(142,257,258,363,259,229,185,307)(151,273,274,309,217,190,312,187)(168,285,286,268,287,368,382,295)(170,289,290,385,291,370,225,292)(180,299,300,388,301,284,381,372)(193,314,308,389,265,313,311,303)(196,317,318,393,319,394,333,347)(202,322,323,396,324,353,378,349)(207,327,328,397,329,398,367,369)(228,320,338,297,339,244,302,357)(230,325,341,321,342,337,296,386)(233,344,330,399,345,332,376,379)(239,350,351,401,352,365,392,361)(242,354,355,343,356,377,366,306)(248,358,359,395,360,281,380,346)(276,373,374,340,375,362,387,310)(288,383,384,391,364,400,390,316);(1,2,6,15,36,83,171,294,149,271,371,286,304,363,323,178,290,163,72,25,4,11,27,62,131,42,91,182,274,372,380,384,389,198,321,300,289,224,153,60,13,32,74,95,38,3,9,22,53,115,221,326,191,56,119,228,340,309,186,129,34,79,165,273,121,19,47,101,196,320,93,185,308,122,230,343,305,183,85,173,81,170,292,373,236,66,140,255,245,87,12,30,69,146,268,282,138,45,7,17,41,90,180,302,354,157,275,154,277,231,50,109,207,330,375,188,253,99,20,49,106,202,325,174,296,285,374,280,379,350,143,263,366,358,177,33,77,160,51,111,212,257,103,24,58,124,233,346,394,397,283,125,234,347,344,112,215,318,113,217,150,272,314,98,193,264,367,356,241,353,383,237,349,398,401,266,176,297,219,299,80,168,288,204,259,141,256,199,59,127,239,351,391,315,261,107,28,64,135,248,218,335,360,247,134,63,132,243,194,316,392,352,238,126,235,205,67,142,260,364,287,167,284,336,357,136,249,361,327,396,348,400,322,128,242,328,144,265,192,313,209,71,151,216,333,250,214,332,393,240,147,269,369,317,395,345,232,123,57,120,229,252,211,110,208,159,76,156,281,355,293,262,365,399,298,387,368,341,226,337,324,201,105,48,102,197,152,276,376,329,206,108,203,213,75,155,278,377,338,301,179,89,40,16,37,84,172,295,267,145,68,29,65,137,158,254,139,251,362,385,291,169,175,43,92,184,306,342,189,311,258,133,244,319,195,100,46,97,190,162,164,78,161,94,187,310,339,227,54,116,222,246,220,114,52,21,8,18,44,96,73,31,70,148,270,370,381,386,181,303,390,359,388,312,210,104,39,86,130,61,26,10,23,55,118,225,279,378,307,331,382,334,166,117,223,200,88,82,35,14,5)(402,403,404,405)
Conjugacy classes & character table
232 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12832, 237);
Finite Group Databasebeta