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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 143 points:
(1,2,3,4,5)(6,43,26,17)(7,9,82,99)(8,81,15,13)(10,88)(11,20,131,132)(12,63,49,18)(14,42,133,23)(16,129,95,68)(19,111,101,60)(21,84,53,33)(22,36,58,57)(24,51,119,78)(25,122,76,50)(27,125,130,138)(28,52,66,97)(29,65,100,71)(30,39,116,38)(31,37,34,35)(32,98,105,86)(40,72,127,64)(41,75,90,103)(44,59,47,45)(46,107,79,56)(48,77,94,73)(54,102,104,139)(55,96,114,137)(61,109,126,117)(62,134,141,108)(67,87,120,143)(69,113,123,80)(70,93,112,118)(74,85)(83,92,106,91)(89,124,110,115)(121,142)(128,136,140,135);(6,8,14)(7,10,13)(9,19,46)(11,23,60)(12,28,68)(15,36,87)(16,40,26)(17,42,45)(18,44,88)(20,38,93)(21,54,43)(22,59,119)(24,56,116)(25,64,73)(27,66,30)(29,72,103)(31,76,112)(32,78,91)(33,65,39)(34,82,86)(35,84,132)(37,79,108)(41,97,71)(47,57,117)(48,80,63)(49,107,83)(50,92,133)(51,90,110)(52,99,102)(53,111,67)(55,74,130)(58,106,131)(61,70,75)(62,123,77)(69,128,100)(81,126,98)(85,113,143)(89,134,95)(94,137,122)(96,109,135)(101,105,125)(104,141,115)(114,129,121)(118,142,139)(120,124,140)(127,138,136)
Conjugacy classes & character table
250 conjugacy classes — view the full character table.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31740, 48);
Finite Group Databasebeta