Finite Group Databasebeta

?

← Prev (#6371490) Next (#6371492) →

C₂²×#1897 #6371491

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

Aliases

Subgroups

7126 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)(9,10,13,16,14,17,12,22)(11,18,21,23,19,24,20,15);(9,11)(10,15,17,23)(12,20)(13,21)(14,19)(16,18,22,24);(6,8)(11,19)(15,23)(18,24)(20,21)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278687);