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Aliases
Splittings
Subgroups
63 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 174 points:
(1,4)(3,5)(6,170,101,90,48,129,33,97,84,138,123,78,13,146,15,100,163,109,58,105,94,162,45,150,11,22,164,80,125,76,66,57,74,12,160,154,110,26,166,82,42,139,51,20,133,36,122,43,155,55,40,117,156,152,108,23,88,28,61,171,137,89,47,127,115,71,32,18,38,158,70,151,106,99,86,67,56,169,91,136,9,120,10,69,161,79,35,75,63,143,72,124,83,65,145,103,168,134,41,81,49,8,174,131,121,16,148,54,102,114,31,62,107,21,165,25,130,116,98,87,132,126,159,14,147,17,37,172,111,59,29,96,85,104,19,113,95,135,44,173,112,68,144,77,34,157,60,149,27,167,7,64,142,52,93,50,39,118,46,92,141,128,119,73,153,140,24,53,30);(1,3,4,2,5)(6,90,131)(7,174,150)(8,122,111)(9,45,48)(10,157,155)(11,172,147)(12,143,52)(13,71,76)(14,43,16)(15,105,99)(17,170,167)(18,142,88)(19,85,138)(20,125,154)(21,102,108)(22,121,60)(23,72,29)(24,106,26)(25,47,41)(28,133,129)(30,164,120)(31,84,118)(32,33,160)(34,151,137)(35,152,95)(36,64,136)(37,149,101)(38,59,91)(39,104,50)(40,110,94)(42,134,44)(46,75,66)(49,158,148)(51,117,146)(53,55,171)(54,169,124)(56,165,79)(57,113,114)(58,168,128)(61,162,80)(62,93,123)(63,97,78)(65,89,126)(67,135,127)(68,112,73)(69,159,70)(74,107,96)(77,145,166)(81,83,161)(82,132,130)(86,141,139)(87,173,109)(92,115,156)(98,119,153)(100,140,103)(116,163,144)
Conjugacy classes & character table
295 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30420, 944);
Finite Group Databasebeta