Finite Group Databasebeta

?

← Prev (#5962) Next (#5964) →

C₂×#1010 #5963

• supersolvable
• metabelian
• solvable
• monomial
• ambivalent

Aliases

Splittings

Subgroups

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1522);