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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 314 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)(120,147,176)(123,150,173)(126,153,170)(129,156,167)(132,159,164)(135,162,161)(138,165,158)(141,168,155)(144,171,152)(146,174,149)(148,178,209)(151,181,206)(154,184,203)(157,187,200)(160,190,197)(163,193,195)(166,179,192)(169,198,189)(172,201,186)(175,204,183)(177,207,180)(182,212,239)(185,215,236)(188,218,233)(191,221,230)(194,224,228)(196,213,226)(199,229,223)(202,231,220)(205,234,217)(208,237,214)(210,240,211)(216,243,264)(219,246,261)(222,249,258)(225,252,256)(227,244,255)(232,257,251)(235,259,248)(238,262,245)(241,265,242)(247,268,283)(250,271,280)(253,274,278)(254,269,277)(260,279,273)(263,281,270)(266,284,267)(272,287,296)(275,290,294)(276,288,293)(282,295,289)(285,297,286)(291,300,304)(292,301,303)(298,305,299)(302,306,307)(309,310)(311,312)(313,314);(1,2,4,8,15,25,38,54,73,95,120,148,179,134,84,46,20,5,9,16,26,39,55,74,96,121,149,180,211,229,165,109,65,33,12,19,29,42,58,77,99,124,152,183,214,242,257,198,137,87,49,22,32,45,61,80,102,127,155,186,217,245,267,279,231,168,112,68,35,48,64,83,105,130,158,189,220,248,270,286,295,259,201,140,90,51,67,86,108,133,161,192,223,251,273,289,299,305,281,234,171,115,70,89,111,136,164,195,226,178,210,241,266,285,298,297,262,204,143,92,114,139,167,197,228,255,212,147,177,208,238,263,282,284,237,174,117,142,170,200,230,256,277,243,181,119,146,175,205,235,260,265,207,145,173,203,233,258,278,293,268,215,150,94,118,144,172,202,232,240,176,206,236,261,280,294,303,287,246,184,122,72,93,116,141,169,199,209,239,264,283,296,304,307,300,271,218,153,97,53,71,91,113,138,166,196,227,254,276,292,302,306,290,249,187,125,75,37,52,69,88,110,135,163,194,225,253,275,291,301,274,221,156,100,56,24,36,50,66,85,107,132,160,191,222,250,272,288,252,190,128,78,40,14,23,34,47,63,82,104,129,157,188,219,247,269,224,159,103,59,27,7,13,21,31,44,60,79,101,126,154,185,216,244,193,131,81,43,17,3,6,11,18,28,41,57,76,98,123,151,182,213,162,106,62,30,10)(308,309,311,313,314,312,310)
Conjugacy classes & character table
525 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12894, 17);
Finite Group Databasebeta