Finite Group Databasebeta

?

← Prev (#72294466) Next (#72294468) →

C₂×#4421183 #72294467

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

Aliases

Subgroups

71821 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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)(15,16)(17,18)(19,20,22,24)(21,23,26,25), (11,13,15,17)(12,14,16,18)(19,20,22,24)(21,25,26,23), (4,6)(8,10)(12,16)(13,17)(19,20,22,24)(21,23,26,25), (7,8)(9,10)(11,13)(12,14)(15,17)(16,18)(19,20)(21,25)(22,24)(23,26), (3,4)(5,6)(7,8)(9,10)(11,14)(12,13)(15,18)(16,17)(19,21,22,26)(20,23,24,25), (1,2));