Finite Group Databasebeta

?

← Prev (#5225) Next (#5227) →

C₂×#836 #5226

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 21 points:

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 785);