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C₂²×#2347 #7625348

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

Aliases

Subgroups

10242 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)(9,10,13,12)(11,15,16,14)(17,18,22,21)(19,24,20,23);(10,12)(14,15)(17,19,22,20)(18,23,21,24);(9,11,13,16)(10,14,12,15)(17,20,22,19)(18,23,21,24);(9,12,13,10)(11,15,16,14)(17,21,22,18)(19,23,20,24)

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7532544);