Finite Group Databasebeta

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D₃×#410 #78693

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 19 points:

(1,2,3)(4,7,8,15)(5,10,11,17)(6,13,14,19)(9,16,12,18);(4,6)(5,9)(7,13)(8,14)(10,16)(11,12)(15,19)(17,18);(4,5)(6,12,14,9)(7,10)(8,11)(13,18,19,16)(15,17);(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, 11269);