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C₃₇×#2205 #17991023

• nilpotent
• supersolvable
• solvable
• monomial

Aliases

Subgroups

224 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)(40,48)(41,51)(42,46)(43,53)(44,49)(45,50)(47,52);(38,40,44,43)(39,45,49,51)(41,52,50,42)(46,48,47,53);(38,41,44,50)(39,46,49,47)(40,42,43,52)(45,53,51,48)

Conjugacy classes & character table

740 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 937);