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C₂⁴×Dic₆ #87552

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

6264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 19 points:

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

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 20128);