Finite Group Databasebeta

?

← Prev (#87194) Next (#87196) →

C₂×#5778 #87195

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 21 points:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 19771);