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Aliases
Splittings
Subgroups
90 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 185 points:
(3,4,5,6,7)(9,11)(10,14)(12,13)(15,16)(18,20)(19,23)(21,26)(22,29)(24,32)(25,31)(27,36)(28,39)(30,41)(33,45)(34,44)(35,43)(37,50)(38,53)(40,55)(42,57)(46,62)(47,61)(48,60)(49,59)(51,68)(52,71)(54,73)(56,75)(58,77)(63,83)(64,82)(65,81)(66,80)(67,79)(69,90)(70,93)(72,95)(74,97)(76,99)(78,101)(84,108)(85,107)(86,106)(87,105)(88,104)(89,103)(91,92)(94,116)(96,118)(98,120)(100,122)(102,124)(109,125)(110,130)(111,129)(112,128)(113,127)(114,126)(115,136)(117,138)(119,140)(121,142)(123,144)(131,145)(132,149)(133,148)(134,147)(135,146)(137,154)(139,156)(141,158)(143,160)(150,161)(151,164)(152,163)(153,162)(155,168)(157,170)(159,172)(165,173)(166,175)(167,174)(169,178)(171,180)(176,181)(177,182)(179,184)(183,185);(1,2)(8,16,11,14,13,12,10,9,15)(17,107,56,80,159,70,174,153,116,165,49,99,64,23,125,40,105,141,51,182,135,138,151,36,122,47,32,102,28,129,119,103,185,114,156,133,53,144,34,45,78,21,149,96,127,179,90,170,112,73,131,25,62,58,43,161,72,147,169,91,180,88,97,110,20,83,42,60,143,52,163,155,136,176,67,120,86,29,108,30,81,121,37,175,137,154,166,50,142,65,41,84,22,106,98,79,181,115,168,152,71,160,48,57,63,18,130,74,104,171,92,178,134,95,150,35,77,46,31,145,54,128,157,69,184,113,118,132,26,101,33,44,123,38,148,139,126,183,89,140,111,39,124,24,61,100,27,164,117,146,177,68,158,87,55,109,19,82,76,59,173,94,162,167,93,172,66,75,85)
Conjugacy classes & character table
7620 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 50);
Finite Group Databasebeta