Finite Group Databasebeta

?

← Prev (#72300215) Next (#72300217) →

C₂³×#2419 #72300216

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

Aliases

Subgroups

128037 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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