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C₂²×#2489 #7627941

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

Aliases

Subgroups

9722 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)(10,12)(11,15)(18,21)(19,23);(5,6,7,8)(9,10,13,12)(11,14,15,16)(17,18)(19,22)(20,21)(23,24);(5,6)(7,8)(9,11)(10,14)(12,16)(13,15);(9,12,13,10)(11,16,15,14)(17,19,20,23)(18,22,21,24)

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, 7535137);