Finite Group Databasebeta

?

← Prev (#72323970) Next (#72323972) →

C₂×#1506866 #72323971

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

Aliases

Subgroups

42593 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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