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C₄₁×#489 #14579957

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 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)(44,47)(45,46)(48,49)(50,51)(52,54)(53,55)(56,57);(43,46)(47,49)(50,52,55,57,56,53,54,51);(42,44,45,48)(43,47,46,49)(50,53,54,57,56,52,55,51)

Conjugacy classes & character table

656 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 170);