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C₄×#2697 #521216

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

Aliases

Subgroups

4298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2,3,4);(9,10,12,14)(11,15,16,13)(17,18)(19,23)(20,22)(21,24);(5,6)(7,8)(9,11,12,16)(10,13,14,15)(17,19)(18,21)(20,24)(22,23);(6,8)(18,22)(21,23);(10,14)(11,16)(19,24)(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, 428412);