Finite Group Databasebeta

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C₂²×#14335 #72290834

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

Aliases

Subgroups

434837 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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