Finite Group Databasebeta

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D₃×#416 #78829

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(5,8,10,9)(6,12,13,17)(7,15,16,18)(11,19,20,14)(21,22,23);(5,7)(6,11)(8,15)(9,18)(10,16)(12,19)(13,20)(14,17);(1,2,3,4)(5,6)(7,14)(8,12)(9,17)(10,13)(11,15)(16,19)(18,20);(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, 11405);