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C₃₇×#2357 #17991175

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

560 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)(38,39,40,41)(42,43,46,45)(44,48,49,47)(50,51,55,54)(52,57,53,56);(43,45)(47,48)(50,52,55,53)(51,56,54,57);(42,44)(43,47)(45,48)(46,49)(50,53,55,52)(51,56,54,57);(42,45,46,43)(44,48,49,47)(50,54,55,51)(52,56,53,57)

Conjugacy classes & character table

1850 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4736, 1089);