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C₃₇×#3061 #17991879

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

484 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)(44,51)(45,49)(46,55)(47,50)(48,53)(52,56)(54,57);(42,44,45,52,47,54,46,53)(43,48,55,57,50,56,49,51);(39,41)(42,43)(44,48)(45,55)(46,49)(47,50)(51,53)(52,57)(54,56);(42,45,47,46)(43,49,50,55)(44,52,54,53)(48,51,56,57)

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, 1793);