Finite Group Databasebeta

?

← Prev (#72334442) Next (#72334444) →

C₂×#72261298 #72334443

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

Aliases

Subgroups

4656160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

392 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((3,4)(5,6)(7,8)(9,10)(11,12,13,14)(15,16)(17,19)(18,20)(21,22), (3,4)(5,6)(7,8,9,10)(11,12,13,14)(17,21)(19,22), (3,4,5,6)(7,8)(9,10)(11,12)(13,14)(15,16,18,20)(17,19,21,22), (4,6)(8,10)(15,17)(16,19)(18,21)(20,22), (8,10), (1,2), (3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,22)(18,20)(19,21));