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C₄×#2010 #359012

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

Aliases

Subgroups

2250 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)(9,12)(10,14)(11,18)(15,20)(17,19);(5,7)(6,10)(8,17)(9,15)(11,20)(12,19)(13,16)(14,18);(10,19)(13,20)

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, 266208);