Finite Group Databasebeta

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C₄₁×#555 #14580023

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

236 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)(45,49)(46,47)(51,52)(55,56);(43,47)(45,48)(50,51,54,52)(53,56,57,55);(42,44,46,49)(43,48,47,45)(50,52,54,51)(53,56,57,55);(42,45,46,48)(43,49,47,44)(50,53,54,57)(51,55,52,56)

Conjugacy classes & character table

1025 conjugacy classes. The character table is too large to display.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 236);