Finite Group Databasebeta

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D₃×#427 #79176

• 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:

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

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, 11752);