Finite Group Databasebeta

?

← Prev (#72298917) Next (#72298919) →

C₂×#9164052 #72298918

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

Aliases

Subgroups

72689 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

178 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)(21,25)(23,26), (12,15)(16,17)(19,20)(21,23)(22,24)(25,26), (4,7)(8,10)(19,20)(21,23)(22,24)(25,26), (4,7)(5,9)(13,18)(16,17)(19,20,22,24)(21,26,25,23), (3,4,6,7)(5,10,9,8)(11,12)(13,16)(14,15)(17,18)(19,20)(21,23)(22,24)(25,26), (3,5)(4,8)(6,9)(7,10)(11,13)(12,16)(14,18)(15,17)(19,21)(20,23)(22,25)(24,26), (1,2));