Finite Group Databasebeta

?

← Prev (#358301) Next (#358303) →

C₂×#11289 #358302

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

Aliases

Subgroups

1762 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 22 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265498);