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C₃₇×#2957 #17991775

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

452 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)(38,39,43,48,44,47,42,56)(40,49,51,45,52,60,57,59)(41,46,55,61,53,62,54,66)(50,63,65,58,64,68,67,69);(38,40)(39,45)(41,50)(42,57)(43,51)(44,52)(46,58)(47,59)(48,60)(49,56)(53,64)(54,67)(55,65)(61,68)(62,69)(63,66);(38,41,43,55,44,53,42,54)(39,46,48,61,47,62,56,66)(40,50,51,65,52,64,57,67)(45,58,60,68,59,69,49,63);(39,47)(41,53)(45,59)(48,56)(49,60)(50,64)(54,55)(65,67)

Conjugacy classes & character table

1628 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1689);