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C₃₇×#2833 #17991651

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(39,42)(43,45)(46,47,50,51)(48,52,53,49)(55,59)(60,62)(61,65)(68,69);(40,44)(43,45)(48,53)(49,52)(54,55,58,59)(56,62,64,60)(57,65,67,61)(63,68,66,69);(38,39)(40,43)(41,42)(44,45)(46,48)(47,49)(50,53)(51,52)(54,56,58,64)(55,60,59,62)(57,66,67,63)(61,69,65,68);(38,40)(39,43)(41,44)(42,45)(46,49)(47,48)(50,52)(51,53)(54,57,58,67)(55,61,59,65)(56,63,64,66)(60,68,62,69)

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, 1565);