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C₃₇×#2069 #17990887

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 53 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)(38,39,43,45,42,46,41,50)(40,47,51,52,48,53,49,44);(38,40,41,49,42,48,43,51)(39,44,45,47,46,52,50,53);(40,48)(41,43)(45,50)(47,53)

Conjugacy classes & character table

851 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 801);