Finite Group Databasebeta

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C₄₁×#544 #14580012

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

206 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(42,43)(44,48)(45,47)(46,49)(50,51,53,55)(52,56,57,54);(42,43,45,47)(44,46,49,48);(42,43)(44,46)(45,47)(48,49)(50,52,53,57)(51,54,55,56);(42,44)(43,46)(45,49)(47,48)

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, 225);