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C₄×#2375 #513769

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

Aliases

Subgroups

4526 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420965);