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C₂³×#2491 #72339193

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

Aliases

Subgroups

148437 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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