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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 291 points:
(2,3,5)(4,7,12)(6,10,9)(8,14,22)(11,17,19)(13,20,16)(15,24,35)(18,27,32)(21,30,29)(23,33,26)(25,37,51)(28,40,48)(31,43,45)(34,46,42)(36,49,39)(38,53,70)(41,56,67)(44,59,64)(47,62,61)(50,65,58)(52,68,55)(54,72,92)(57,75,89)(60,78,86)(63,81,83)(66,84,80)(69,87,77)(71,90,74)(73,94,117)(76,97,114)(79,100,111)(82,103,108)(85,106,105)(88,109,102)(91,112,99)(93,115,96)(95,119,145)(98,122,142)(101,125,139)(104,128,136)(107,131,133)(110,134,130)(113,137,127)(116,140,124)(118,143,121)(120,147,174)(123,149,172)(126,152,169)(129,155,166)(132,158,163)(135,161,160)(138,164,157)(141,167,154)(144,170,151)(146,173,148)(150,177,199)(153,178,198)(156,181,195)(159,184,192)(162,187,189)(165,190,186)(168,193,183)(171,196,180)(175,200,176)(179,201,220)(182,202,219)(185,205,216)(188,208,213)(191,211,210)(194,214,207)(197,217,204)(203,221,237)(206,222,236)(209,225,233)(212,228,230)(215,231,227)(218,234,224)(223,238,251)(226,239,250)(229,242,247)(232,245,244)(235,248,241)(240,252,262)(243,253,261)(246,256,258)(249,259,255)(254,263,270)(257,264,269)(260,267,266)(265,271,275)(268,272,274)(273,276,277)(278,279,281,280,282,284,283,285,286)(287,288,289,290,291);(1,2,4,8,15,25,38,54,73,95,120,143,92,114,139,166,192,213,230,244,255,252,222,181,125,75,37,52,69,88,110,135,162,188,209,226,240,248,214,164,109,65,33,12,19,29,42,58,77,99,124,151,147,175,200,145,172,198,219,236,250,261,269,274,271,253,225,184,128,78,40,14,23,34,47,63,82,104,129,156,182,203,217,167,112,68,35,48,64,83,105,130,157,183,204,201,149,94,118,144,171,197,218,235,249,260,268,273,272,256,228,187,131,81,43,17,3,6,11,18,28,41,57,76,98,123,150,170,115,70,89,111,136,163,189,210,227,241,238,202,152,97,53,71,91,113,138,165,191,212,229,243,254,259,231,190,134,84,46,20,5,9,16,26,39,55,74,96,121,148,176,173,117,142,169,195,216,233,247,258,266,263,239,205,155,100,56,24,36,50,66,85,107,132,159,185,206,223,234,193,137,87,49,22,32,45,61,80,102,127,154,180,177,119,146,174,199,220,237,251,262,270,275,277,276,264,242,208,158,103,59,27,7,13,21,31,44,60,79,101,126,153,179,196,140,90,51,67,86,108,133,160,186,207,224,221,178,122,72,93,116,141,168,194,215,232,246,257,265,267,245,211,161,106,62,30,10)
Conjugacy classes & character table
1425 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12465, 2);
Finite Group Databasebeta