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C₂²×#1931 #6371664

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

Aliases

Subgroups

3802 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6278860);