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C₂²×#2724 #7633491

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

Aliases

Subgroups

10578 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540687);