Finite Group Databasebeta

?

← Prev (#72299257) Next (#72299259) →

C₂×#2814158 #72299258

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

Aliases

Subgroups

54913 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

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

Conjugacy classes & character table

160 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)(5,6)(7,8,9,10)(12,14)(15,16)(17,21)(18,19)(20,22), (4,6)(8,10)(11,12)(13,14)(15,16)(17,20)(18,19)(21,22), (4,6)(7,8,9,10)(16,19)(20,21), (8,10)(15,17)(16,20)(18,22)(19,21), (3,4)(5,6)(7,8)(9,10)(15,16)(17,21)(18,19)(20,22), (1,2));