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C₄×#2699 #521217

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

Aliases

Subgroups

3694 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)(11,13,15,16)(17,18,20,22)(19,21,23,24);(5,6)(7,8)(9,10)(11,13)(12,14)(15,16)(17,19,20,23)(18,21,22,24);(6,8)(9,11,12,15)(10,13,14,16)(18,22)(21,24);(10,14)(13,16)(18,22)(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, 428413);