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C₃₇×#2263 #17991081

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

112 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)(40,44)(41,53)(42,56)(43,45)(46,49)(47,50)(48,54)(51,63)(52,57)(55,69)(58,65)(59,64)(60,66)(61,67)(62,68);(39,44)(40,49)(41,50)(42,54)(45,57)(46,47)(48,63)(51,68)(52,66)(53,58)(55,67)(56,59)(60,61)(62,69)(64,65);(39,45)(44,57)(46,60)(47,61)(48,56)(53,69)(58,62)(59,63)

Conjugacy classes & character table

962 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 995);