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C₃₇×#2845 #17991663

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

340 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)(38,39,41,43)(40,42,44,45)(46,47,50,49)(48,51,52,53)(55,58)(59,60);(40,44)(42,45)(47,49)(51,53)(54,55,57,58)(56,59,61,60);(38,39)(40,42)(41,43)(44,45)(46,48,50,52)(47,51,49,53)(54,55)(56,60)(57,58)(59,61);(38,40)(39,42)(41,44)(43,45)(46,49,50,47)(48,51,52,53)(54,56,57,61)(55,59,58,60)

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, 1577);