Finite Group Databasebeta

?

← Prev (#7633427) Next (#7633429) →

C₂²×#2695 #7633428

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

Aliases

Subgroups

10578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540624);