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C₃₇×#2838 #17991656

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

366 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)(39,42)(43,45)(47,48)(51,52)(54,55,58,60)(56,57,59,61);(40,44)(43,45)(46,47,50,48)(49,51,53,52)(54,56)(55,57)(58,59)(60,61);(38,39,41,42)(40,43,44,45)(46,48,50,47)(49,51,53,52)(54,57)(55,59)(56,60)(58,61);(38,40)(39,43)(41,44)(42,45)(46,49,50,53)(47,51,48,52)

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, 1570);