Finite Group Databasebeta

?

← Prev (#84075) Next (#84077) →

C₂×#5237 #84076

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

756 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)(9,17)(10,15)(12,20)(13,14)(16,18)(19,21);(1,2)(8,15)(11,14)(16,17)(19,20);(4,5)(6,7,9,12,10,13,18,21)(8,14,16,20,15,11,17,19);(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, 16652);