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C₃₇×#488 #14557153

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 61 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)(40,43)(41,42)(44,45)(46,47)(48,56)(49,52)(50,60)(51,55)(53,58)(54,57)(59,61);(39,42)(43,45)(46,48,57,59,51,58,50,49)(47,52,60,53,55,61,54,56);(38,40,41,44)(39,43,42,45)(46,49,50,58,51,59,57,48)(47,53,54,52,55,56,60,61)

Conjugacy classes & character table

814 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 169);