Finite Group Databasebeta

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C₄₇×#560 #15688815

• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 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)(50,57)(51,56)(52,54)(53,59)(55,61)(58,62)(60,63);(48,50)(49,53)(51,59)(52,60)(54,62)(55,63)(56,57)(58,61);(49,54)(50,58)(53,57)(55,56)(59,60)(62,63);(49,55)(50,59)(53,62)(54,56)(57,63)(58,60)

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, 241);