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C₄×#819 #69790

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

228 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 23 points:

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

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, 2366);