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C₂²×#2019 #6431779

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

Aliases

Subgroups

7622 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)(11,18,21,23)(12,15,22,16)(14,19,24,20);(6,8)(9,11)(10,14)(12,19)(13,21)(15,18)(16,23)(17,24)(20,22);(10,15)(11,19)(12,22)(16,17)(18,23)(20,21)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6338975);