Finite Group Databasebeta

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C₄₁×#401 #14579869

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

118 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 65 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)(44,48)(46,49)(51,54)(55,56)(58,59,61,63)(60,64,65,62);(42,43,45,47)(44,49,48,46)(50,51,53,54)(52,56,57,55)(58,59)(60,64)(61,63)(62,65);(42,44)(43,46)(45,48)(47,49)(50,52,53,57)(51,55,54,56)(58,60,61,65)(59,62,63,64)

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, 82);