Finite Group Databasebeta

?

← Prev (#72334530) Next (#72334532) →

C₂×#517469 #72334531

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

Aliases

Subgroups

75629 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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((4,6)(7,8,10,9)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22), (3,4)(5,6)(8,9)(11,12,13,14)(16,20)(18,22), (4,6)(7,8,10,9)(11,12)(13,14)(15,17)(16,18)(19,21)(20,22), (3,4)(5,6)(7,9,10,8)(11,12)(13,14)(15,17)(16,18)(19,21)(20,22), (1,2), (15,18)(16,21)(17,20)(19,22));