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C₂²×#2374 #7625378

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

Aliases

Subgroups

11490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532574);