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C₄×#2011 #359036

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

Aliases

Subgroups

2874 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 266232);