Finite Group Databasebeta

?

← Prev (#72298702) Next (#72298704) →

C₂×#7672751 #72298703

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

Aliases

Subgroups

136501 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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)(13,17)(16,18), (7,8)(9,10)(13,17)(16,18), (4,6)(12,15)(13,17), (3,4)(5,6)(12,15)(13,17), (11,12,14,15)(13,16,17,18), (11,13)(12,16)(14,17)(15,18), (1,2));