Finite Group Databasebeta

?

← Prev (#72298864) Next (#72298866) →

C₂×#7679583 #72298865

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

Aliases

Subgroups

128959 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

220 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((8,10)(11,12)(13,15)(14,17)(16,18), (3,4,5,6)(7,8)(9,10)(11,12,14,17)(13,15,18,16), (3,4,5,6)(11,12)(13,15)(14,17)(16,18), (3,4,5,6)(11,13,14,18)(12,15,17,16), (3,4)(5,6)(11,12)(13,15)(14,17)(16,18), (3,4)(5,6)(11,13)(12,16)(14,18)(15,17), (1,2));