Finite Group Databasebeta

?

← Prev (#72294586) Next (#72294588) →

C₂×#1419378 #72294587

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

Aliases

Subgroups

69653 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

184 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)(13,17)(14,15)(16,18)(20,23)(24,26), (3,4,5,6)(7,8,9,10)(12,15)(13,18)(21,25)(24,26), (3,4)(5,6)(7,8)(9,10)(19,20,22,23)(21,24,25,26), (7,8)(9,10)(11,12)(13,16)(14,15)(17,18)(19,20)(21,24)(22,23)(25,26), (3,4)(5,6)(7,8)(9,10)(11,13)(12,16)(14,18)(15,17)(19,21)(20,24)(22,25)(23,26), (1,2));