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C₃₇×#2438 #17991256

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

528 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)(42,43)(44,48)(45,47)(46,49)(50,51,54,57)(52,56,53,55);(39,41)(42,43,45,47)(44,46,49,48)(50,52,54,53)(51,55,57,56);(38,39)(40,41)(42,43)(44,46)(45,47)(48,49)(50,53,54,52)(51,56,57,55);(42,44)(43,46)(45,49)(47,48)(50,51)(52,55)(53,56)(54,57)

Conjugacy classes & character table

1406 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1170);