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C₃₇×#508 #14557173

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

84 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)(40,49)(41,46)(42,54)(43,58)(44,48)(45,51)(47,56)(50,65)(52,66)(53,64)(55,60)(57,68)(59,63)(61,69)(62,67);(38,40)(39,45)(41,50)(42,55)(43,59)(44,52)(46,60)(47,63)(48,62)(49,54)(51,56)(53,67)(57,69)(58,61)(64,65)(66,68);(38,41,44,43)(39,46,48,58)(40,50,52,59)(42,53,57,56)(45,60,62,61)(47,54,64,68)(49,65,66,63)(51,55,67,69)

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, 189);