Finite Group Databasebeta

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D₃×#464 #80596

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

57 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 13172);