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D₃×#536 #86353

• supersolvable
• metabelian
• solvable
• monomial
• stem
• rational
• ambivalent

Aliases

Splittings

Subgroups

1512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 23 points:

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

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, 18929);