Finite Group Databasebeta

?

← Prev (#72298748) Next (#72298750) →

C₂×#7631292 #72298749

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

Aliases

Subgroups

129097 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 18 points:

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

Conjugacy classes & character table

244 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)(8,10)(13,16)(14,17), (3,4,5,6)(7,8)(9,10)(11,12,15,18)(13,17,16,14), (11,13)(12,14)(15,16)(17,18), (3,4)(5,6)(11,14)(12,16)(13,18)(15,17), (11,14)(12,13)(15,17)(16,18), (11,13)(12,17)(14,18)(15,16), (1,2));