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C₃₇×#1426 #17990244

• nilpotent
• metacyclic
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 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)(39,44,46,57)(40,49)(41,53)(42,54)(45,60)(47,61,64,69)(48,67,65,59)(50,55)(51,63)(52,62)(56,68,66,58);(38,39,45,61,41,47,40,44,54,65,49,58,50,56,60,67,43,46,63,69,55,64,52,57,42,48,62,68,53,66,51,59)

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, 158);