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C₃₇×#2649 #17991467

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 61 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)(39,42)(43,45)(46,47)(48,51)(49,50)(52,53)(54,55,58,57)(56,60,61,59);(47,50)(51,52)(56,61)(59,60);(38,39)(40,43)(41,42)(44,45)(46,47)(48,52)(49,50)(51,53)(54,56)(55,59)(57,60)(58,61);(38,40,41,44)(39,43,42,45)(46,48)(47,51)(49,53)(50,52)(54,57,58,55)(56,60,61,59)

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, 1381);