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C₃₇×#2836 #17991654

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

358 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)(46,47,50,49)(48,51,52,53)(54,55)(56,60)(57,61)(58,59);(40,44)(43,45)(47,49)(48,52)(55,59)(57,60);(38,39,41,42)(40,43,44,45)(46,48)(47,51)(49,53)(50,52)(54,56)(55,60)(57,59)(58,61);(38,40)(39,43)(41,44)(42,45)(46,49,50,47)(48,51,52,53)(54,57,58,60)(55,61,59,56)

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, 1568);