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Aliases
Splittings
Subgroups
16 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 178 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)(73,94,112)(76,96,113)(79,99,110)(82,102,107)(85,105,104)(88,108,101)(91,111,98)(93,114,95)(97,118,131)(100,120,132)(103,122,130)(106,125,127)(109,128,124)(115,133,119)(116,134,117)(121,137,146)(123,138,147)(126,140,145)(129,143,142)(135,148,136)(139,149,155)(141,150,156)(144,152,154)(151,157,160)(153,158,161)(159,162,163)(164,165,166,167,168,169,170,171,172,173,174,175,176)(177,178);(1,2,4,8,15,25,38,54,73,87,49,22,32,45,61,80,101,94,116,135,148,114,70,89,110,130,145,154,149,120,75,37,52,69,88,109,129,144,153,159,158,140,102,59,27,7,13,21,31,44,60,79,100,121,128,84,46,20,5,9,16,26,39,55,74,95,117,111,68,35,48,64,83,104,124,118,72,93,115,134,92,113,132,147,156,161,157,138,99,56,24,36,50,66,85,106,126,141,151,152,125,81,43,17,3,6,11,18,28,41,57,76,97,108,65,33,12,19,29,42,58,77,98,119,136,133,90,51,67,86,107,127,142,137,96,53,71,91,112,131,146,155,160,163,162,150,122,78,40,14,23,34,47,63,82,103,123,139,143,105,62,30,10)
Conjugacy classes & character table
1482 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12714, 2);
Finite Group Databasebeta