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C₄₁×#497 #14579965

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

124 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)(46,47,50,53)(48,54,55,61)(49,57,58,52)(51,59,60,56);(46,48,49,56,50,55,58,59)(47,51,52,54,53,60,57,61);(42,43,44,45)(48,55)(51,60)(54,61)(56,59)

Conjugacy classes & character table

656 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 178);