Finite Group Databasebeta

?

← Prev (#87193) Next (#87195) →

C₂×#5777 #87194

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2)(3,4,5)(6,8,10,14)(7,12,11,20)(9,18,19,16)(13,21,17,15);(1,2)(6,7)(8,15)(9,17)(10,11)(12,16)(13,19)(14,21)(18,20);(7,11)(12,20)(13,17)(15,21);(4,5)(8,14)(12,20)(15,21)(16,18);(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, 19770);