Finite Group Databasebeta

?

← Prev (#72339236) Next (#72339238) →

C₂³×#2500 #72339237

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

Aliases

Subgroups

123621 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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