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C₃₇×#2070 #17990888

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

196 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)(38,39,42,56,43,47,58,46)(40,48,50,44,51,64,68,60)(41,52,54,61,55,45,57,62)(49,65,66,59,53,63,67,69);(38,40,42,50,43,51,58,68)(39,44,46,48,47,60,56,64)(41,53,54,67,55,49,57,66)(45,59,61,65,52,69,62,63);(38,41,43,55)(39,45,47,52)(40,49,51,53)(42,57,58,54)(44,59,60,69)(46,62,56,61)(48,63,64,65)(50,67,68,66)

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, 802);