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C₄×#2622 #515190

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

Aliases

Subgroups

4532 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 422386);