Finite Group Databasebeta

?

← Prev (#72334469) Next (#72334471) →

C₂×#759861 #72334470

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

Aliases

Subgroups

70953 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

208 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((3,4)(5,6)(7,8,9,10)(12,15)(16,18)(19,20,23,24)(21,25,26,22), (4,6)(8,10)(13,17)(16,18)(21,26)(22,25), (3,4)(5,6)(7,8)(9,10)(11,12,14,15)(13,18,17,16)(19,21)(20,22)(23,26)(24,25), (1,2), (8,10)(11,12)(13,18)(14,15)(16,17)(19,20)(21,25)(22,26)(23,24), (3,4)(5,6)(7,8)(9,10)(11,13,14,17)(12,16,15,18)(19,22,23,25)(20,21,24,26));