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Aliases
Splittings
Subgroups
12 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 174 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174);(8,10,9,11)(13,174)(14,173)(15,172)(16,171)(17,170)(18,169)(19,168)(20,167)(21,166)(22,165)(23,164)(24,163)(25,162)(26,161)(27,160)(28,159)(29,158)(30,157)(31,156)(32,155)(33,154)(34,153)(35,152)(36,151)(37,150)(38,149)(39,148)(40,147)(41,146)(42,145)(43,144)(44,143)(45,142)(46,141)(47,140)(48,139)(49,138)(50,137)(51,136)(52,135)(53,134)(54,133)(55,132)(56,131)(57,130)(58,129)(59,128)(60,127)(61,126)(62,125)(63,124)(64,123)(65,122)(66,121)(67,120)(68,119)(69,118)(70,117)(71,116)(72,115)(73,114)(74,113)(75,112)(76,111)(77,110)(78,109)(79,108)(80,107)(81,106)(82,105)(83,104)(84,103)(85,102)(86,101)(87,100)(88,99)(89,98)(90,97)(91,96)(92,95)(93,94)
Conjugacy classes & character table
1162 conjugacy classes. The character table is too large to display.
Relationships
| maximal subgroup of | C3×C7×Dic163, C7×Dic489, C7×(C163⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C7×Dic163, C7×(C163⋊C3)⋊C4, ΓL(1,𝔽8)×Dic163, … |
| maximal quotient of | C3×C7×Dic163, C7×Dic489, C5×C7×Dic163, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4564, 3);
Finite Group Databasebeta