Finite Group Databasebeta

?

← Prev (#80224) Next (#80226) →

D₃×#452 #80225

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

760 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(2,4)(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)(5,6,10,13)(7,14,16,19)(8,12,9,17)(11,18,20,15);(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, 12801);