Finite Group Databasebeta

?

← Prev (#72301674) Next (#72301676) →

C₂³×#62818 #72301675

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

Aliases

Subgroups

9724840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 9 generators on 22 points:

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

Conjugacy classes & character table

608 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((3,4), (5,6), (1,2)(3,4)(5,6), (7,8,12,13)(9,14,10,11)(15,16,19,21)(17,20,22,18), (7,9,12,10)(8,11,13,14)(15,17)(16,18)(19,22)(20,21), (9,10)(11,14)(15,17)(16,20)(18,21)(19,22), (15,17,19,22)(16,20,21,18), (7,10,12,9)(8,11,13,14)(15,17)(16,18)(19,22)(20,21), (7,11)(8,10)(9,13)(12,14)(15,18)(16,17)(19,20)(21,22));