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C₄₁×#495 #14579963

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41)(43,45)(46,47)(48,54)(49,57)(50,52)(51,55)(53,58)(56,60)(59,61);(46,48,49,55,50,56,58,61)(47,51,53,54,52,59,57,60);(42,43,44,45)(47,52)(51,59)(53,57)(54,60)

Conjugacy classes & character table

902 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 176);