Finite Group Databasebeta

?

← Prev (#72302565) Next (#72302567) →

C₂×#843227 #72302566

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

Aliases

Subgroups

31703 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2)(7,8,9,10)(11,12,15,14)(13,16,17,18);(4,6)(7,8)(9,10)(12,14)(16,18)(21,25)(24,26);(7,8)(9,10)(12,14)(13,17)(19,20,23,22)(21,24,25,26);(3,4)(5,6)(7,8,9,10)(12,14)(16,18);(3,4)(5,6)(7,8)(9,10)(11,13,15,17)(12,16,14,18)(19,21)(20,24)(22,26)(23,25);(3,4)(5,6)(7,8)(9,10)(11,14,15,12)(13,16,17,18)(19,22,23,20)(21,26,25,24)

Conjugacy classes & character table

196 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((1,2)(7,8,9,10)(11,12,15,14)(13,16,17,18), (4,6)(7,8)(9,10)(12,14)(16,18)(21,25)(24,26), (7,8)(9,10)(12,14)(13,17)(19,20,23,22)(21,24,25,26), (3,4)(5,6)(7,8,9,10)(12,14)(16,18), (3,4)(5,6)(7,8)(9,10)(11,13,15,17)(12,16,14,18)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(7,8)(9,10)(11,14,15,12)(13,16,17,18)(19,22,23,20)(21,26,25,24));