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C₂²×#2096 #6432404

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

Aliases

Subgroups

3950 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

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

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, 6339600);