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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 403 points:
(2,7,38,41,71,4,17,92,99,35,9,43,202,14,86,22,104,6,36,40,55,3,15,16,97)(5,28,157,23,136,12,70,54,58,156,30,161,130,67,133,75,114,27,56,268,105,11,68,134,57)(8,48,226,64,163,20,115,26,151,235,50,240,65,112,359,120,269,47,236,367,137,19,113,246,150)(10,60,260,335,125,25,142,200,52,256,62,91,21,126,358,146,201,53,230,381,132,24,128,265,395)(13,66,288,387,320,33,154,389,291,314,82,289,339,178,141,184,388,80,287,208,286,32,153,373,344)(18,109,263,299,168,46,231,166,103,302,110,228,300,223,378,185,356,108,262,83,321,45,129,254,186)(29,165,392,401,294,73,298,346,210,313,167,393,380,295,371,301,264,164,391,247,366,72,296,379,276)(31,176,330,277,131,78,307,328,248,266,177,315,119,311,355,179,362,175,329,79,267,77,195,334,180)(34,188,399,174,397,85,323,221,310,364,190,308,353,241,124,237,319,187,198,255,361,84,322,143,309)(37,197,139,96,348,90,59,273,212,368,199,140,337,249,171,333,275,196,292,297,347,89,325,272,211)(39,207,398,100,155,95,343,261,217,224,209,390,377,341,259,332,385,206,400,376,281,94,342,386,216)(42,220,93,118,238,102,284,204,138,331,222,365,189,271,149,244,305,219,147,117,357,101,352,49,245)(44,227,285,232,270,107,152,354,135,290,229,225,326,159,172,213,191,69,76,98,87,106,160,173,214)(51,63,193,340,375,123,88,327,349,338,253,194,215,203,293,257,282,252,162,127,374,122,148,205,258)(61,279,192,233,303,145,383,111,318,396,280,360,183,370,363,384,382,278,239,345,274,144,372,312,283)(74,304,316,116,336,170,394,317,243,234,306,350,158,182,250,218,324,81,121,369,351,169,181,251,242)(402,403);(1,2,5,13,34,14,37,91,200,220,67,118,247,363,78,178,176,312,285,115,241,233,270,150,283,7,18,19,49,119,249,90,117,246,302,395,258,299,394,55,132,267,378,25,63,149,242,157,110,232,28,71,163,294,169,305,214,322,102,209,346,140,276,35,87,192,251,371,112,237,329,301,4,10,26,66,155,43,105,226,355,353,271,175,236,360,180,45,92,203,213,243,342,354,399,367,359,20,51,124,188,324,136,201,336,382,396,383,376,27,69,134,122,227,125,65,152,286,32,81,183,319,73,168,303,86,156,273,252,372,223,295,94,208,345,235,182,262,128,261,365,139,274,153,12,31,79,181,317,107,197,331,184,320,161,292,361,216,316,338,204,339,381,279,172,240,222,50,121,53,129,264,219,3,8,21,54,131,40,98,215,335,343,159,291,356,375,154,256,314,369,388,250,370,170,99,17,44,24,61,52,127,259,327,397,248,177,313,398,391,263,379,321,374,108,230,33,83,187,278,293,60,143,77,38,93,205,199,334,68,158,289,340,296,347,75,89,198,332,123,254,130,265,298,280,191,151,284,185,109,133,269,364,393,165,6,16,42,103,224,47,114,239,349,389,164,297,217,46,111,234,288,390,142,113,238,362,400,287,304,326,207,72,166,231,190,325,257,85,62,147,84,189,145,281,386,95,210,193,245,366,160,229,358,333,211,348,173,308,318,380,255,260,266,82,15,39,96,22,56,135,202,337,244,311,384,300,196,194,328,350,104,225,272,306,392,385,309,315,351,48,116,144,30,76,174,11,29,74,171,307,101,221,344,352,401,268,146,282,387,36,88,195,167,80,126,253,373,212,57,137,64,9,23,59,141,277,341,368,310,206,290,275,323,377,97,186,41,100,218,58,138,70,162,148,120,179,106,228,357,330)
Conjugacy classes & character table
82 conjugacy classes — view the full character table.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20050, 9);
Finite Group Databasebeta