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C₂²×#2085 #6432209

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

Aliases

Subgroups

3022 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)(11,16)(12,14)(13,15)(18,21)(22,24);(9,11,13,12)(10,14,15,16)(18,22)(20,23)(21,24);(6,8)(9,12,13,11)(10,14,15,16)(17,18)(19,21)(20,24)(22,23)

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339405);