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C₃₇×#510 #14557175

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 69 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)(40,48)(41,52)(42,57)(43,45)(44,49)(46,55)(47,54)(50,68)(51,65)(53,63)(56,64)(58,62)(59,67)(60,69)(61,66);(38,40,43,51)(39,44,45,59)(41,53,56,69)(42,58,54,50)(46,62,61,68)(47,63,57,60)(48,64,65,52)(49,66,67,55);(39,45)(44,59)(46,61)(47,57)(48,65)(52,64)(60,63)(62,68)

Conjugacy classes & character table

592 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2368, 191);