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C₂×C₃×Dic₁₂ #64028

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

131 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 24 points:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(288, 676);