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C₃₇×#2949 #17991767

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

492 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)(38,39,41,40)(42,43)(44,50)(45,53)(46,48)(47,51)(49,55)(52,57)(54,56);(42,44,46,52)(43,47,48,56)(45,54,55,51)(49,57,53,50);(38,40,41,39)(42,43)(44,47)(45,49)(46,48)(50,51)(52,56)(53,55)(54,57);(43,48)(47,56)(49,53)(50,57)

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, 1681);