Finite Group Databasebeta

?

← Prev (#72296006) Next (#72296008) →

C₂²×#34176 #72296007

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

Aliases

Subgroups

205941 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

352 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((9,10)(11,14)(12,13)(15,16)(17,18,21,22)(19,20,23,24), (5,6,8,7)(10,13)(14,15)(18,22)(19,23), (17,19)(18,20)(21,23)(22,24), (9,10)(11,15)(12,13)(14,16)(17,19)(18,20)(21,23)(22,24), (5,7,8,6)(9,11)(10,14)(12,16)(13,15)(17,20)(18,23)(19,22)(21,24), (3,4), (1,2)(3,4));