Finite Group Databasebeta

?

← Prev (#72291554) Next (#72291556) →

C₂³×#2420 #72291555

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

Aliases

Subgroups

136725 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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