Finite Group Databasebeta

?

← Prev (#10574210) Next (#10574212) →

C₂³×#446 #10574211

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

Aliases

Subgroups

8242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481407);