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C₂²×#2859 #7633333

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

Aliases

Subgroups

9154 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540529);