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C₂³×Dic₁₂ #87151

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

1464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 25 points:

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

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19727);