Finite Group Databasebeta

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C₂×#4556 #71992

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 21 points:

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

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 4568);