Finite Group Databasebeta

?

← Prev (#73342) Next (#73344) →

C₂×#4657 #73343

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 21 points:

(1,2)(3,4,5)(6,7)(8,9)(10,12,13,11)(14,16)(15,18)(17,20)(19,21);(1,2)(7,9)(10,11)(12,13)(14,15,17,19)(16,18,20,21);(4,5)(10,11,13,12)(16,20)(18,21);(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, 5919);