Finite Group Databasebeta

?

← Prev (#72298727) Next (#72298729) →

C₂×#531611 #72298728

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

Aliases

Subgroups

81769 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 18 points:

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

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