Finite Group Databasebeta

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C₂²×#8145 #72319659

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

Aliases

Subgroups

14037 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

Conjugacy classes & character table

448 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((1,2)(3,4)(5,6)(7,8), (1,2), (1,2)(3,4)(9,10,11,13,12,14,15,16)(17,18,20,19,21,22,24,23), (3,4), (6,8)(17,19,20,22,21,23,24,18));