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C₂²×#2952 #10574149

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

Aliases

Subgroups

10858 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 10481345);