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D₃×#562 #87107

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

Aliases

Splittings

Subgroups

1152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 19 points:

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

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, 19683);