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C₂²×#1937 #6371702

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

Aliases

Subgroups

3542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278898);