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C₃₇×#2951 #17991769

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

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, 1683);