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C₂²×#1929 #6371657

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

Aliases

Subgroups

3434 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

(1,2);(3,4);(6,7)(9,10,13,17,14,12,21,16)(11,15,19,23,20,18,24,22);(5,6,8,7)(9,11,13,19,14,20,21,24)(10,15,17,23,12,18,16,22);(5,7,8,6)(9,12)(10,14)(11,18)(13,16)(15,20)(17,21)(19,22)(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, 6278853);