Finite Group Databasebeta

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C₄₇×#484 #15688739

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 63 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)(48,49)(50,53)(51,52)(54,55)(56,57,58,60)(59,61,63,62);(49,52)(53,55)(57,60)(61,62);(48,50,51,54)(49,53,52,55)(57,61)(59,63)(60,62)

Conjugacy classes & character table

893 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3008, 165);