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C₂²×#1785 #6370699

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

Aliases

Subgroups

18434 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)(9,10,13,18,14,17,12,16)(11,19,20,24,21,15,22,23);(9,11)(10,15)(12,20)(13,22)(14,21)(16,23)(17,19)(18,24);(6,8)(9,12,14,13)(10,16,17,18)(11,20,21,22)(15,23,19,24)

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, 6277895);