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Aliases
Splittings
Subgroups
36 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 149 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)(54,72,91)(57,75,88)(60,78,86)(63,81,83)(66,84,80)(69,73,77)(71,89,74)(76,94,109)(79,97,107)(82,100,105)(85,103,102)(87,95,99)(90,108,96)(92,110,93)(98,113,123)(101,115,122)(104,118,120)(106,114,117)(111,124,112)(116,125,132)(119,127,131)(121,126,129)(128,133,137)(130,134,136)(135,138,139)(141,142,143)(144,146,145)(148,149);(1,2,4,8,15,25,38,54,73,49,22,32,45,61,80,99,72,92,111,110,70,88,107,122,131,136,125,97,56,24,36,50,66,85,104,119,128,134,118,81,43,17,3,6,11,18,28,41,57,76,95,65,33,12,19,29,42,58,77,96,112,124,89,51,67,86,105,120,129,113,75,37,52,69,87,106,121,130,135,138,127,100,59,27,7,13,21,31,44,60,79,98,114,84,46,20,5,9,16,26,39,55,74,93,108,68,35,48,64,83,102,117,94,53,71,90,91,109,123,132,137,139,133,115,78,40,14,23,34,47,63,82,101,116,126,103,62,30,10)(140,141,143,145,142,144,146)(147,148,149)
Conjugacy classes & character table
981 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17514, 54);
Finite Group Databasebeta