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D₃×#732 #92278

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 2 generators on 30 points:

(2,3)(4,25,24,15,14,13,7,6,30)(5,12,23,10,20,19,11,9,22)(8,28,27,21,18,26,17,16,29);(1,2,3)(4,5,8)(6,12,16)(7,11,17)(9,18,14)(10,21,15)(13,23,26)(19,29,30)(20,28,25)(22,27,24)

Conjugacy classes & character table

51 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 123);