Finite Group Databasebeta

?

← Prev (#72289349) Next (#72289351) →

C₂²×D₄×#95 #72289350

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

Aliases

Subgroups

144349 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

Conjugacy classes & character table

400 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((17,18,19,20), (6,8)(10,12)(13,14,16,15)(17,18,19,20), (17,18)(19,20), (5,6)(7,8)(9,10,11,12)(13,15,16,14), (3,4), (1,2)(3,4));