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C₂²×Dic₁₂ #5742

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

258 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 23 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1301);