Finite Group Databasebeta

?

← Prev (#6431777) Next (#6431779) →

C₂²×#2018 #6431778

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

Aliases

Subgroups

8158 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)(11,19)(12,17)(13,16)(14,18)(15,20)(21,24)(22,23);(6,8)(9,11)(10,15)(12,21)(13,20)(14,22)(16,23)(17,19)(18,24);(10,16)(11,20)(12,13)(17,18)(19,23)(21,22)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338974);