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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 426 points:
(4,5)(7,11,12,30,35,106,132,8,9,17,19,55,69,135)(10,24,25,91,96,62,210,14,15,46,48,153,117,118)(13,40,41,148,152,381,134,21,22,78,80,259,265,71)(16,53,54,186,70,50,51,27,28,102,104,36,26,100)(18,63,64,212,217,415,369,32,33,119,121,339,344,238)(20,72,73,239,243,236,237,37,38,136,138,357,133,367)(23,85,86,278,282,321,337,43,44,161,163,391,302,411)(29,107,108,325,229,346,409,56,57,195,197,218,316,420)(31,115,75,76,250,194,362,60,61,39,143,144,231,249)(34,126,127,311,312,154,155,66,67,227,187,389,81,211)(42,157,158,387,273,274,368,82,83,269,271,159,385,334)(45,77,166,256,376,377,101,88,89,146,285,251,406,52)(47,173,174,394,147,379,380,93,94,294,283,257,258,370)(49,182,183,113,109,330,305,98,99,268,59,199,200,405)(58,202,169,399,400,162,392,110,111,289,290,395,279,280)(65,222,223,349,233,234,248,123,124,221,351,131,364,142)(68,139,232,342,372,373,308,129,130,245,363,244,374,185)(74,128,247,92,266,272,310,140,141,230,170,171,246,340)(79,262,263,207,208,343,417,150,151,156,116,216,335,375)(84,165,276,317,419,191,206,87,160,190,345,410,319,320)(90,287,288,416,270,336,425,167,168,397,333,209,360,418)(95,299,298,291,388,332,284,176,177,403,396,286,205,338)(97,303,292,293,103,314,315,179,180,172,393,188,189,408)(105,322,323,253,254,404,198,192,193,213,145,300,331,329)(112,260,281,326,304,295,313,204,164,382,196,181,201,401)(114,261,309,178,252,125,355,149,203,383,301,267,225,226)(120,341,324,350,277,327,422,214,215,412,413,354,390,414)(122,347,348,358,359,306,307,219,220,421,228,424,184,407)(137,328,255,175,402,318,378,240,241,361,296,297,398,386)(224,423,365,366,356,242,384,352,353,235,426,275,264,371);(1,2)(3,4,5)(6,7,10,16,29,58,112,205,333,226,356,273,157,270,207,115,206,334,367,414,421,171,259,150,22,42,84,85,162,281,393,380,369,132,134,70,30,59,114,41,81,156,268,386,285,396,289,167,88,43,21,11,18,34,68,131,235,312,387,413,124,224,354,165,284,155,210,337,377,405,304,179,91,117,60,12,20,39,77,147,163,283,395,417,362,248,140,72,137,242,262,366,371,407,317,339,297,383,308,51,101,50,24,47,95,178,302,319,186,310,323,64,122,221,86,164,80,153,267,250,329,195,306,182,225,123,63,120,216,287,282,349,409,425,373,230,361,253,143,251,274,381,234,241,325,189,316,174,292,170,25,49,35,53,103,190,318,397,412,322,245,363,341,419,423,392,111,203,303,177,300,404,330,236,106,194,141,126,228,360,399,258,220,315,359,243,127,229,212,166,286,158,272,130,136,192,102,187,313,403,296,173,295,199,107,196,327,415,343,372,239,138,244,335,344,390,326,57,109,201,94,175,298,401,311,54,105,73,139,246,269,388,146,121,218,227,357,424,408,347,379,290,336,358,67,128,231,69,133,200,331,254,299,180,261,202,280,353,410,215,342,232,193,324,288,398,276,188,28,55,98,46,92,172,294,346,314,197,328,364,265,385,376,76,145,255,247,374,418,420,351,391,168,208,214,33,65,125,99,184,108,198,144,252,96,148,260,161,223,219,119,213,340,104,191,321,301,176,93,15,26,52,100,185,309,402,217,345,307,384,426,151,264,240,38,74,142,249,375,400,394,278,257,89,75,37,17,31,62,48,97,181,305,406,411,118,211,338,160,277,352,222,350,271,389,365,233,129,66,32,9,13,23,45,90,169,291,256,378,183,263,154,78,149,113,19,36,71,135,238,370,293,382,279,44,87,82,40,79,152,266,348,422,237,368,320,61,116,209,83,159,275,355,416,332,204,110,56,27,14,8)
Conjugacy classes & character table
222 conjugacy classes — view the full character table.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35364, 41);
Finite Group Databasebeta