Finite Group Databasebeta

?

← Prev (#7625252) Next (#7625254) →

C₂²×C₄×#126 #7625253

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

Aliases

Subgroups

10314 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

(1,2);(3,4);(5,6,7,8);(10,14)(11,18)(16,23)(17,21)(19,22)(20,24);(9,10,15,21)(11,16,22,23)(12,14,13,17)(18,24,19,20);(9,11,12,19)(10,16,14,20)(13,18,15,22)(17,24,21,23)

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, 7532449);