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C₂²×#1963 #6371960

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

Aliases

Subgroups

5714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279156);