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D₅₃×#2155 #27537101

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 85 points:

(1,4,7,6)(2,9,11,21)(3,13,15,16)(5,17,20,19)(8,22,23,32)(10,18,24,31)(12,25,26,30)(14,27,28,29)(33,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35);(1,3,5,14,6,16,19,29,7,15,20,28,4,13,17,27)(2,8,10,12,9,22,18,25,11,23,24,26,21,32,31,30);(1,2)(3,12,15,26)(4,9)(5,18)(6,21)(7,11)(8,14,23,28)(10,19)(13,25,16,30)(17,24)(20,31)(22,27,32,29);(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)

Conjugacy classes & character table

896 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 322577);