Finite Group Databasebeta

?

← Prev (#72301427) Next (#72301429) →

C₂²×#35540 #72301428

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

Aliases

Subgroups

114733 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 24 points:

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

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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