Finite Group Databasebeta

?

← Prev (#6369739) Next (#6369741) →

C₂³×#338 #6369740

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

Aliases

Subgroups

8010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6276936);