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C₄₁×#510 #14579978

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 73 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)(44,52)(45,56)(46,61)(47,49)(48,53)(50,59)(51,58)(54,72)(55,69)(57,67)(60,68)(62,66)(63,71)(64,73)(65,70);(42,44,47,55)(43,48,49,63)(45,57,60,73)(46,62,58,54)(50,66,65,72)(51,67,61,64)(52,68,69,56)(53,70,71,59);(43,49)(48,63)(50,65)(51,61)(52,69)(56,68)(64,67)(66,72)

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, 191);