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C₂³×#14134 #72325800

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

Aliases

Subgroups

3908024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 22 points:

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