Finite Group Databasebeta

?

← Prev (#72299603) Next (#72299605) →

C₂×#72298030 #72299604

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

Aliases

Subgroups

At least 14772 conjugacy classes of subgroups; only the 38160 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

308 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)(12,14)(15,16)(17,20)(18,19)(21,22), (4,6)(11,12)(13,14), (8,10)(16,19)(17,21), (4,6)(7,8)(9,10), (3,4)(5,6)(15,16)(17,22)(18,19)(20,21), (3,4)(5,6)(15,17)(16,20)(18,21)(19,22), (1,2));