Finite Group Databasebeta

?

← Prev (#72325233) Next (#72325235) →

C₂×#2110317 #72325234

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

Aliases

Subgroups

45861 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

160 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)(13,17)(14,18)(15,16)(19,20,23,21)(22,24,26,25), (4,6)(7,8)(9,10)(12,16)(14,17)(19,20,23,21)(22,24,26,25), (7,8)(9,10)(20,21)(22,26), (7,8,9,10)(11,13)(12,17)(14,16)(15,18)(19,21,23,20)(22,24,26,25), (1,2), (3,4,5,6)(7,8)(9,10)(11,14,15,17)(12,18,16,13)(19,22,23,26)(20,24,21,25));