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C₄₁×#488 #14579956

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 65 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)(42,43)(44,47)(45,46)(48,49)(50,51)(52,60)(53,56)(54,64)(55,59)(57,62)(58,61)(63,65);(43,46)(47,49)(50,52,61,63,55,62,54,53)(51,56,64,57,59,65,58,60);(42,44,45,48)(43,47,46,49)(50,53,54,62,55,63,61,52)(51,57,58,56,59,60,64,65)

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, 169);