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C₂³×#2682 #72325230

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

Aliases

Subgroups

162613 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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