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C₂²×#2690 #7633423

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

Aliases

Subgroups

9330 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540619);