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C₃₇×#2103 #17990921

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 69 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)(38,39,42,47,43,48,44,59)(40,49,51,61,53,64,52,45)(41,54,56,68,57,46,58,63)(50,62,65,69,66,67,55,60);(38,40,44,51,43,53,42,52)(39,45,59,49,48,61,47,64)(41,55,58,50,57,65,56,66)(46,62,68,69,54,67,63,60);(38,41,42,56,43,57,44,58)(39,46,47,63,48,54,59,68)(40,50,51,65,53,66,52,55)(45,60,49,62,61,69,64,67)

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, 835);