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Aliases
Splittings
Subgroups
66 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 367 points:
(1,2,4,7,11,16,22,29,37,46,56,67,79,92,106,121,137,154,172,3,5,8,12,17,23,30,38,47,57,68,80,93,107,122,138,155,173,191,6,9,13,18,24,31,39,48,58,69,81,94,108,123,139,156,174,192,209,10,14,19,25,32,40,49,59,70,82,95,109,124,140,157,175,193,210,226,15,20,26,33,41,50,60,71,83,96,110,125,141,158,176,194,211,227,242,21,27,34,42,51,61,72,84,97,111,126,142,159,177,195,212,228,243,257,28,35,43,52,62,73,85,98,112,127,143,160,178,196,213,229,244,258,271,36,44,53,63,74,86,99,113,128,144,161,179,197,214,230,245,259,272,284,45,54,64,75,87,100,114,129,145,162,180,198,215,231,246,260,273,285,296,55,65,76,88,101,115,130,146,163,181,199,216,232,247,261,274,286,297,307,66,77,89,102,116,131,147,164,182,200,217,233,248,262,275,287,298,308,317,78,90,103,117,132,148,165,183,201,218,234,249,263,276,288,299,309,318,326,91,104,118,133,149,166,184,202,219,235,250,264,277,289,300,310,319,327,334,105,119,134,150,167,185,203,220,236,251,265,278,290,301,311,320,328,335,341,120,135,151,168,186,204,221,237,252,266,279,291,302,312,321,329,336,342,347,136,152,169,187,205,222,238,253,267,280,292,303,313,322,330,337,343,348,352,153,170,188,206,223,239,254,268,281,293,304,314,323,331,338,344,349,353,356,171,189,207,224,240,255,269,282,294,305,315,324,332,339,345,350,354,357,359,190,208,225,241,256,270,283,295,306,316,325,333,340,346,351,355,358,360,361)(362,363,364)(366,367);(363,364)(365,366,367)
Conjugacy classes & character table
3249 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12996, 41);
Finite Group Databasebeta