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C₂²×#3275 #10576044

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

Aliases

Subgroups

11286 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)(12,21,22,15)(14,19,23,20);(9,11,13,18)(10,14,16,23)(12,19,22,20)(15,24,21,17);(6,8)(11,18)(14,23)(17,24)(19,20);(11,19)(12,22)(14,24)(15,21)(17,23)(18,20)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483240);