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C₂²×#3285 #10576030

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

Aliases

Subgroups

10814 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)(10,14)(11,17)(12,20)(15,18)(16,21)(23,24);(9,10,13,16)(11,18,17,23)(12,21,20,14)(15,22,24,19);(6,8);(9,11,13,17)(10,15,16,24)(12,22,20,19)(14,23,21,18)

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, 10483226);