Finite Group Databasebeta

?

← Prev (#84084) Next (#84086) →

C₂×#5240 #84085

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

788 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(3,4,5)(6,8)(7,11)(9,14)(10,15)(12,17)(13,18)(16,20)(19,21);(1,2)(6,7,10,13)(8,11,15,18)(9,12,16,19)(14,17,20,21);(4,5)(8,14,15,20)(9,16)(11,17,18,21)(12,19);(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, 16661);