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C₂³×#1336 #72319035

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

Aliases

Subgroups

7733 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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