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C₂²×#3287 #10576033

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

Aliases

Subgroups

11202 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)(10,15)(11,13)(12,19)(16,20)(17,21)(23,24);(9,10,14,17)(11,15,13,21)(12,20,19,23)(16,22,24,18);(6,8)(9,11,14,13)(10,15,17,21)(12,18,19,22)(16,23,24,20);(9,12,14,19)(10,16,17,24)(11,18,13,22)(15,23,21,20)

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483229);