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C₂²×#2723 #7633469

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

Aliases

Subgroups

10374 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)(17,18,22,24)(19,21,20,23);(6,8)(10,13)(11,15)(17,19,22,20)(18,23,24,21);(5,6)(7,8)(9,10)(11,14)(12,13)(15,16)(17,20,22,19)(18,23,24,21);(9,11,12,15)(10,14,13,16)(17,21,22,23)(18,19,24,20)

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, 7540665);