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C₃₇×#2829 #17991647

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

450 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)(48,51)(49,50)(52,53)(54,55,58,57)(56,59,60,61);(40,44)(43,45)(47,50)(48,52)(55,57)(59,61);(38,39)(40,43)(41,42)(44,45)(46,47)(48,53)(49,50)(51,52)(54,56)(55,59)(57,61)(58,60);(38,40)(39,43)(41,44)(42,45)(46,48,49,52)(47,51,50,53)(54,57,58,55)(56,59,60,61)

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, 1561);