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C₂²×#2481 #7627825

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

Aliases

Subgroups

11814 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7535021);