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C₂²×#2688 #7633426

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

Aliases

Subgroups

14150 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)(19,22)(20,24)(21,23);(6,8)(10,11)(12,16)(17,19,21,24)(18,22,23,20);(5,6)(7,8)(9,11,13,10)(12,15,16,14)(17,19)(18,20)(21,24)(22,23);(9,12)(10,14)(11,15)(13,16)(17,20)(18,19)(21,22)(23,24)

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, 7540622);