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C₂²×#2720 #7633467

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

Aliases

Subgroups

9634 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7540663);