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C₂²×#2447 #7627862

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

Aliases

Subgroups

11610 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7535058);