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C₃₇×#1407 #17990225

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

98 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)(38,39)(40,48,50,63)(41,52,53,68)(42,55,57,46)(43,47)(44,49,58,65)(45,54)(51,61,56,64)(59,66,60,67)(62,69);(38,40,43,51)(39,44,47,60)(41,49,53,67)(42,56,57,50)(45,61,62,48)(46,58,55,59)(52,64,68,63)(54,65,69,66)

Conjugacy classes & character table

518 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 139);