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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 304 points:
(2,6,4,3)(5,15,9,8)(7,11,13,12)(10,28,18,17)(14,24,22,21)(16,20,26,25)(19,45,31,30)(23,41,35,34)(27,37,39,38)(29,33,43,42)(32,66,48,47)(36,62,52,51)(40,58,56,55)(44,54,60,59)(46,50,64,63)(49,91,69,68)(53,87,73,72)(57,83,77,76)(61,79,81,80)(65,75,85,84)(67,71,89,88)(70,120,94,93)(74,116,98,97)(78,112,102,101)(82,108,106,105)(86,104,110,109)(90,100,114,113)(92,96,118,117)(95,153,123,122)(99,149,127,126)(103,145,131,130)(107,141,135,134)(111,137,139,138)(115,133,143,142)(119,129,147,146)(121,125,151,150)(124,187,156,155)(128,183,160,159)(132,179,157,162)(136,175,165,164)(140,171,169,168)(144,167,173,172)(148,163,177,176)(152,161,181,180)(154,158,185,184)(166,207,193,192)(170,203,197,196)(174,199,201,200)(178,195,205,204)(182,191,209,208)(186,190,212,211)(188,189,214,194)(198,230,220,219)(202,226,224,223)(206,222,228,227)(210,218,232,231)(213,217,235,234)(215,216,237,221)(225,249,243,242)(229,245,247,246)(233,241,251,250)(236,240,254,253)(238,239,256,244)(248,264,262,261)(252,260,266,265)(255,259,269,268)(257,258,271,263)(267,275,277,276)(270,274,280,279)(272,273,282,278)(281,285,287,286)(283,284,289,288)(290,291,293,292)(294,295,296,297,298,299,300,301,302,303,304);(1,2,5,10,19,32,49,70,95,124,157,131,102,77,56,39,26,15,24,37,54,75,100,129,161,190,216,220,197,169,139,110,85,64,45,62,83,108,137,167,195,218,240,258,262,247,228,205,177,147,118,91,116,145,175,203,226,245,260,274,284,287,280,269,254,235,212,185,153,183,155,188,215,238,257,272,283,290,292,286,276,261,242,219,192,162,126,93,121,152,182,210,233,252,267,278,268,250,227,200,168,134,101,72,47,67,90,115,144,174,202,225,244,234,208,176,142,109,80,55,34,17,29,44,61,82,107,136,166,194,184,150,117,88,63,42,25,12,3,7,14,23,36,53,74,99,128,160,127,98,73,52,35,22,13,6,11,20,33,50,71,96,125,158,189,193,165,135,106,81,60,43,28,41,58,79,104,133,163,191,217,239,243,224,201,173,143,114,89,66,87,112,141,171,199,222,241,259,273,277,266,251,232,209,181,151,120,149,179,207,230,249,264,275,285,291,293,289,282,271,256,237,214,187,159,122,154,186,213,236,255,270,281,288,279,265,246,223,196,164,130,97,68,92,119,148,178,206,229,248,263,253,231,204,172,138,105,76,51,30,46,65,86,111,140,170,198,221,211,180,146,113,84,59,38,21,8,16,27,40,57,78,103,132,156,123,94,69,48,31,18,9,4)
Conjugacy classes & character table
847 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12892, 6);
Finite Group Databasebeta