Finite Group Databasebeta

?

← Prev (#6369753) Next (#6369755) →

C₂²×#1738 #6369754

• 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 24 points:

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

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, 6276950);