Finite Group Databasebeta

?

← Prev (#72294968) Next (#72294970) →

C₂×#3069121 #72294969

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

Aliases

Subgroups

40751 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

148 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((7,8)(9,10)(11,12,15,16)(13,14,17,18)(19,20)(21,24)(22,25)(23,26), (7,8,9,10)(13,17)(14,18)(19,21)(20,23)(22,26)(24,25), (4,6)(7,8)(9,10)(12,16)(14,18)(19,21,22,26)(20,23,25,24), (11,13,15,17)(12,14,16,18)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(11,14)(12,13)(15,18)(16,17)(19,20)(21,24)(22,25)(23,26), (1,2));