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C₃₇×#2814 #17991632

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 57 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)(43,46)(47,49)(50,51,54,57)(52,53,56,55);(39,41)(43,46)(44,48)(50,52,54,56)(51,55,57,53);(38,39)(40,41)(42,43)(44,47)(45,46)(48,49)(50,52)(51,53)(54,56)(55,57);(42,44)(43,47)(45,48)(46,49)(50,53)(51,56)(52,57)(54,55)

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, 1546);