Finite Group Databasebeta

?

← Prev (#72289146) Next (#72289148) →

C₂³×#2849 #72289147

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

Aliases

Subgroups

502477 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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

Conjugacy classes & character table

352 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((8,10)(11,12,13,14)(15,16,18,20)(17,19,21,22), (15,16)(17,19)(18,20)(21,22), (11,12)(13,14)(15,16)(17,19)(18,20)(21,22), (3,4), (5,6), (1,2)(3,4)(5,6), (7,8)(9,10)(11,12)(13,14)(15,17,18,21)(16,19,20,22));