Finite Group Databasebeta

?

← Prev (#72300206) Next (#72300208) →

C₂³×#2686 #72300207

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

Aliases

Subgroups

126653 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

256 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((8,10)(11,12,15,16)(13,17,18,14)(21,25)(23,26), (7,8)(9,10)(19,20,22,24)(21,26,25,23), (11,13,15,18)(12,14,16,17)(19,20)(21,23)(22,24)(25,26), (11,14)(12,13)(15,17)(16,18)(19,21)(20,23)(22,25)(24,26), (3,4), (5,6), (1,2)(3,4)(5,6));