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Aliases
Splittings
Subgroups
40 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 184 points:
(1,2,3,4,5)(6,7)(8,10,11,9)(13,14,15,17)(16,19,20,26)(18,23,24,22)(21,28,29,39)(25,32,33,35)(27,36,37,31)(30,41,42,56)(34,45,46,52)(38,49,50,48)(40,53,54,44)(43,58,59,77)(47,62,63,73)(51,66,67,69)(55,70,71,65)(57,74,75,61)(60,79,80,102)(64,83,84,98)(68,87,88,94)(72,91,92,90)(76,95,96,86)(78,99,100,82)(81,104,105,129)(85,108,109,126)(89,112,113,123)(93,116,117,119)(97,120,121,115)(101,106,124,111)(103,127,128,107)(110,130,131,148)(114,133,134,147)(118,137,138,144)(122,141,142,140)(125,132,145,136)(135,149,150,163)(139,152,153,162)(143,156,157,159)(146,151,160,155)(154,164,165,174)(158,167,168,173)(161,166,171,170)(169,175,176,181)(172,177,178,180)(179,182,183,184);(6,8,11)(7,10,9)(12,13,16,21,30,43,60,81,106,95,70,49,32,19,27,38,51,68,89,114,135,151,141,116,87,62,41,57,76,97,122,143,158,169,177,167,152,133,108,79,103,129,148,163,174,181,184,183,178,171,160,145,124,100,77,98,123,144,159,170,165,153,138,117,92,71,54,39,52,69,90,115,136,131,109,84,63,46,33,24,17,22,31,44,61,82,107,127,99,74,53,36,23,14,18,25,34,47,64,85,110,132,120,91,66,45,28,40,55,72,93,118,139,154,166,156,137,112,83,58,78,101,125,146,161,172,179,182,175,164,149,130,104,128,102,126,147,162,173,180,176,168,157,142,121,96,75,56,73,94,119,140,155,150,134,113,88,67,50,37,26,35,48,65,86,111,105,80,59,42,29,20,15)
Conjugacy classes & character table
1965 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31140, 51);
Finite Group Databasebeta