Finite Group Databasebeta

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C₂²×#778474 #72321318

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

Aliases

Subgroups

At least 7686 conjugacy classes of subgroups; only the 47376 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

392 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((3,4), (9,10,11,12)(13,14,15,16), (5,6,7,8)(13,14)(15,16)(17,18,20,22)(19,23,24,21), (9,10)(11,12)(13,14)(15,16)(17,18)(19,21)(20,22)(23,24), (1,2)(3,4), (6,8)(9,10)(11,12)(13,14)(15,16)(17,19,20,24)(18,21,22,23), (5,6)(7,8)(17,18)(19,23)(20,22)(21,24));