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C₃₇×#2725 #17991543

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

434 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)(43,44)(47,48)(50,51,54,57)(52,55,56,53);(39,41)(42,43,46,44)(45,48,49,47)(50,52,54,56)(51,55,57,53);(38,39)(40,41)(42,44,46,43)(45,48,49,47)(50,53,54,55)(51,56,57,52);(42,45,46,49)(43,47,44,48)(50,51)(52,55)(53,56)(54,57)

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1457);