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C₄×#400 #13864

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

Aliases

Subgroups

699 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 24 points:

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

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 6852);