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C₂²×#10993 #72315006

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

Aliases

Subgroups

49149 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

(6,8)(9,10,12,16,13,14,19,21)(11,15,18,22,17,20,23,24);(5,6)(7,8)(10,14)(11,17)(12,19)(22,24);(5,6)(7,8)(10,15)(14,20)(16,22)(21,24);(1,2);(3,4)

Conjugacy classes & character table

208 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((6,8)(9,10,12,16,13,14,19,21)(11,15,18,22,17,20,23,24), (5,6)(7,8)(10,14)(11,17)(12,19)(22,24), (5,6)(7,8)(10,15)(14,20)(16,22)(21,24), (1,2), (3,4));