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C₂²×#2345 #7625343

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

Aliases

Subgroups

11594 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7532539);