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C₂²×#3056 #10574893

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

Aliases

Subgroups

11290 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)(11,17,18,24)(12,20,21,15)(14,22,23,19);(9,11,12,19,13,18,21,22)(10,14,15,17,16,23,20,24);(6,8);(11,18)(14,23)(17,24)(19,22)

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, 10482089);