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C₄×#2121 #492991

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

Aliases

Subgroups

1513 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400187);