Finite Group Databasebeta

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D₃×#568 #87165

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 19 points:

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

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19741);