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C₂²×#2398 #7627699

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

Aliases

Subgroups

12322 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7534895);