Finite Group Databasebeta

?

← Prev (#72324523) Next (#72324525) →

C₂³×#2409 #72324524

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

Aliases

Subgroups

321685 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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)(15,16,18,20)(17,21,22,19), (8,10)(12,14)(15,16,18,20)(17,21,22,19), (3,4), (5,6), (12,14)(15,17,18,22)(16,19,20,21), (1,2)(3,4)(5,6), (7,8)(9,10)(11,12)(13,14)(15,16)(17,19)(18,20)(21,22));