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C₂³×#2422 #72339234

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

Aliases

Subgroups

157445 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

304 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((7,8,10,9)(12,13)(16,19)(17,21), (8,9)(11,12,14,13)(15,16)(17,20)(18,19)(21,22), (8,9)(15,16)(17,20)(18,19)(21,22), (3,4), (5,6), (1,2)(3,4)(5,6), (7,9,10,8)(11,13,14,12)(15,17,18,21)(16,20,19,22));