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C₂²×#2421 #7627868

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

Aliases

Subgroups

10042 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535064);