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C₂²×#2629 #7627769

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

Aliases

Subgroups

9634 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7534965);