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C₂²×#1445 #514010

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

Aliases

Subgroups

11074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 421206);