Finite Group Databasebeta

?

← Prev (#72324450) Next (#72324452) →

C₂×#521655 #72324451

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

Aliases

Subgroups

74613 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

232 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((12,15)(16,18)(20,21)(22,26), (4,6)(8,10)(13,17)(16,18)(19,20,23,21)(22,25,26,24), (13,17)(16,18)(22,26)(24,25), (4,6)(8,10)(11,12)(13,18)(14,15)(16,17)(19,21,23,20)(22,25,26,24), (1,2), (3,4,5,6)(7,8)(9,10)(11,13,14,17)(12,16,15,18)(19,22)(20,24)(21,25)(23,26));