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C₂²×#2685 #7633421

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

Aliases

Subgroups

17286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540617);