Finite Group Databasebeta

?

← Prev (#72293813) Next (#72293815) →

C₂²×#845492 #72293814

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

Aliases

Subgroups

753108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

368 conjugacy classes. The character table is too large to display.

Relationships

GAP

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

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