Finite Group Databasebeta

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C₂²×#686214 #72321325

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

Aliases

Subgroups

1051392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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