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Aliases
Splittings
Subgroups
30 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 367 points:
(1,2)(3,5,6,4)(7,8,10,13,17,22,28,35,43,52,62,73,85,98,112,127,143,160,178,9,11,14,18,23,29,36,44,53,63,74,86,99,113,128,144,161,179,197,12,15,19,24,30,37,45,54,64,75,87,100,114,129,145,162,180,198,215,16,20,25,31,38,46,55,65,76,88,101,115,130,146,163,181,199,216,232,21,26,32,39,47,56,66,77,89,102,116,131,147,164,182,200,217,233,248,27,33,40,48,57,67,78,90,103,117,132,148,165,183,201,218,234,249,263,34,41,49,58,68,79,91,104,118,133,149,166,184,202,219,235,250,264,277,42,50,59,69,80,92,105,119,134,150,167,185,203,220,236,251,265,278,290,51,60,70,81,93,106,120,135,151,168,186,204,221,237,252,266,279,291,302,61,71,82,94,107,121,136,152,169,187,205,222,238,253,267,280,292,303,313,72,83,95,108,122,137,153,170,188,206,223,239,254,268,281,293,304,314,323,84,96,109,123,138,154,171,189,207,224,240,255,269,282,294,305,315,324,332,97,110,124,139,155,172,190,208,225,241,256,270,283,295,306,316,325,333,340,111,125,140,156,173,191,209,226,242,257,271,284,296,307,317,326,334,341,347,126,141,157,174,192,210,227,243,258,272,285,297,308,318,327,335,342,348,353,142,158,175,193,211,228,244,259,273,286,298,309,319,328,336,343,349,354,358,159,176,194,212,229,245,260,274,287,299,310,320,329,337,344,350,355,359,362,177,195,213,230,246,261,275,288,300,311,321,330,338,345,351,356,360,363,365,196,214,231,247,262,276,289,301,312,322,331,339,346,352,357,361,364,366,367);(1,3,6)(2,5,4)
Conjugacy classes & character table
2166 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12996, 37);
Finite Group Databasebeta