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C₄×#2888 #6369827

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

Aliases

Subgroups

5257 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6277023);