Finite Group Databasebeta

?

← Prev (#72289510) Next (#72289512) →

C₂³×#2361 #72289511

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

Aliases

Subgroups

208149 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 18 points:

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

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