Finite Group Databasebeta

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C₄₁×#560 #14580028

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

252 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)(44,51)(45,50)(46,48)(47,53)(49,55)(52,56)(54,57);(42,44)(43,47)(45,53)(46,54)(48,56)(49,57)(50,51)(52,55);(43,48)(44,52)(47,51)(49,50)(53,54)(56,57);(43,49)(44,53)(47,56)(48,50)(51,57)(52,54)

Conjugacy classes & character table

779 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 241);