Finite Group Databasebeta

?

← Prev (#14580009) Next (#14580011) →

C₄₁×#542 #14580010

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

216 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)(52,56)(54,57);(42,43,45,47)(44,46,49,48)(50,51,53,55)(52,54,56,57);(42,43)(44,46)(45,47)(48,49)(50,52)(51,54)(53,56)(55,57);(42,44,45,49)(43,46,47,48)

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, 223);