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C₄₁×H(3,𝔽₄) #14580029

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

260 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)(42,43,46,49)(44,51,52,48)(45,53,55,57)(47,50,56,54);(42,44,46,52)(43,48,49,51)(45,54,55,50)(47,53,56,57);(42,45)(43,44)(46,55)(47,48)(49,52)(50,53)(51,56)(54,57);(42,44)(43,45)(46,52)(47,53)(48,50)(49,55)(51,54)(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, 242);