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C₃₇×#2574 #17991392

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

436 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)(48,50)(49,52)(51,53)(54,55,57,59)(56,58,60,61);(47,48)(51,52)(54,55,57,59)(56,58,60,61);(38,39)(40,43)(41,42)(44,45)(46,48,50,47)(49,52,53,51)(54,55)(56,58)(57,59)(60,61);(38,40,41,44)(39,43,42,45)(46,49,50,53)(47,51,48,52)(54,56,57,60)(55,58,59,61)

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, 1306);