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C₂²×#2640 #7627772

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

Aliases

Subgroups

10490 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7534968);