Finite Group Databasebeta

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Dic₃×#137 #83964

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 16540);