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C₃₇×#541 #14557206

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(40,44)(42,45)(46,47,50,53)(48,51,56,54)(49,57,58,52)(55,60,61,59);(38,39,41,43)(40,42,44,45)(46,47)(48,54)(49,52)(50,53)(51,56)(55,60)(57,58)(59,61);(38,40)(39,42)(41,44)(43,45)(46,48)(47,51)(49,55)(50,56)(52,59)(53,54)(57,60)(58,61);(46,49,50,58)(47,52,53,57)(48,55,56,61)(51,59,54,60)

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, 222);