Finite Group Databasebeta

?

← Prev (#72289182) Next (#72289184) →

C₂×#639822 #72289183

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

Aliases

Subgroups

159389 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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