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C₂²×#2470 #7627887

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

Aliases

Subgroups

11290 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(3,4);(10,13)(11,15)(17,18)(19,23)(20,22)(21,24);(6,8)(9,10)(11,14)(12,13)(15,16)(17,18,20,22)(19,21,24,23);(5,6)(7,8)(9,10)(11,14)(12,13)(15,16)(17,18)(19,21)(20,22)(23,24);(9,11,12,15)(10,14,13,16)(17,19)(18,21)(20,24)(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, 7535083);