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M₁₆×#135 #6345023

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

Aliases

Subgroups

1873 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6252219);