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C₂²×#2624 #7627765

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

Aliases

Subgroups

11738 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

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, 7534961);