Finite Group Databasebeta

?

← Prev (#72237415) Next (#72237417) →

C₂²×#59126 #72237416

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

Aliases

Subgroups

220725 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 16 points:

(3,4);(1,2)(3,4);(5,6)(7,8)(10,12)(13,14)(15,16);(5,6)(7,8)(10,12)(14,15);(5,6,7,8)(10,12)(13,15,16,14);(6,8)(9,10)(11,12);(5,6)(7,8)

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((3,4), (1,2)(3,4), (5,6)(7,8)(10,12)(13,14)(15,16), (5,6)(7,8)(10,12)(14,15), (5,6,7,8)(10,12)(13,15,16,14), (6,8)(9,10)(11,12), (5,6)(7,8));