Finite Group Databasebeta

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D₃×#413 #78713

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

756 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 19 points:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 11289);