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D₃×#733 #92279

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

72 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)(4,11,21,7,10,8,15,5,17)(6,9,28,14,20,16,25,12,18)(13,22,29,24,19,26,30,23,27)

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, 124);