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C₄₁×#472 #14579940

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 57 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)(43,47)(44,51)(45,48)(50,55)(52,53)(54,56);(42,43,48,55,46,50,45,47)(44,49,51,56,53,57,52,54);(42,44)(43,49)(45,52)(46,53)(47,54)(48,51)(50,57)(55,56)

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, 153);