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C₃₇×#1534 #17990352

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

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, 266);