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C₃₇×#3201 #17992019

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

390 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)(40,44)(41,43)(42,45)(48,54)(49,56)(51,58)(53,60)(55,57)(59,61);(38,40)(39,42)(41,45)(43,44)(46,47)(48,51)(49,53)(50,52)(54,58)(55,59)(56,60)(57,61);(40,45)(42,44)(46,48,50,55)(47,51,52,59)(49,57,56,54)(53,61,60,58);(39,43)(42,44)(47,52)(51,59)(53,60)(58,61)

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, 1933);