Finite Group Databasebeta

?

← Prev (#72334633) Next (#72334635) →

C₂×#4418493 #72334634

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

Aliases

Subgroups

70759 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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