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C₄₁×#491 #14579959

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

90 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)(50,51,56,61)(52,58,63,64)(53,57,62,65)(54,60,55,59);(43,46)(47,49)(50,52,54,53,56,63,55,62)(51,57,59,58,61,65,60,64);(42,44,45,48)(43,47,46,49)(50,53,54,63,56,62,55,52)(51,58,59,65,61,64,60,57)

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, 172);