Finite Group Databasebeta

?

← Prev (#72325166) Next (#72325168) →

C₂³×#43021 #72325167

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

Aliases

Subgroups

1318648 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 26 points:

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

Conjugacy classes & character table

464 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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