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C₂²×#2851 #7633320

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

Aliases

Subgroups

12106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540516);