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Aliases
Splittings
Subgroups
24 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 159 points:
(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52)(53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159);(5,52)(6,51)(7,50)(8,49)(9,48)(10,47)(11,46)(12,45)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(54,159)(55,158)(56,157)(57,156)(58,155)(59,154)(60,153)(61,152)(62,151)(63,150)(64,149)(65,148)(66,147)(67,146)(68,145)(69,144)(70,143)(71,142)(72,141)(73,140)(74,139)(75,138)(76,137)(77,136)(78,135)(79,134)(80,133)(81,132)(82,131)(83,130)(84,129)(85,128)(86,127)(87,126)(88,125)(89,124)(90,123)(91,122)(92,121)(93,120)(94,119)(95,118)(96,117)(97,116)(98,115)(99,114)(100,113)(101,112)(102,111)(103,110)(104,109)(105,108)(106,107)
Conjugacy classes & character table
7869 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31458, 5);
Finite Group Databasebeta