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C₂²×#2660 #7627780

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

Aliases

Subgroups

9010 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7534976);