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C₂²×#2639 #7627718

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

Aliases

Subgroups

12786 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7534914);