Finite Group Databasebeta

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D₃×#424 #79079

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

(1,2,3)(10,16)(13,19)(17,22)(20,23);(4,5,6,7)(8,10)(9,13)(11,17)(12,16)(14,20)(15,19)(18,22)(21,23);(5,7)(8,9,11,14,12,15,18,21)(10,13,17,20,16,19,22,23);(2,3)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 11655);