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C₄₁×#499 #14579967

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

86 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)(42,43,45,47)(44,48,49,46)(50,51,53,55)(52,58,59,65)(54,62,61,57)(56,64,63,60);(42,44,45,49)(43,46,47,48)(51,55)(56,63)(57,62)(58,65);(50,52,54,60,53,59,61,64)(51,56,57,58,55,63,62,65)

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, 180);