Finite Group Databasebeta

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C₄₁×#562 #14580030

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

220 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)(43,46)(44,48)(50,51)(52,56)(53,54)(55,57);(43,46)(47,49)(51,54)(55,56);(42,43)(44,47)(45,46)(48,49)(50,52,53,57)(51,55,54,56);(42,44)(43,47)(45,48)(46,49)(50,51)(52,55)(53,54)(56,57)

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, 243);