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C₄×#2005 #359062

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

Aliases

Subgroups

2036 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 266258);