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C₂²×C₄×SD₃₂ #7622593

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

Aliases

Subgroups

2214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7529789);