Finite Group Databasebeta

?

← Prev (#3425) Next (#3427) →

C₂×#519 #3426

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

744 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

(1,2);(3,4,5,6)(8,12)(10,18)(13,15)(16,22);(7,8,11,12)(9,15,17,13)(10,14,18,19)(16,21,22,20);(7,9,11,17)(8,13,12,15)(10,16,18,22)(14,20,19,21);(7,10)(8,14)(9,16)(11,18)(12,19)(13,20)(15,21)(17,22)

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(128, 2158);