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C₂²×#2058 #6431972

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

Aliases

Subgroups

4998 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6339168);