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C₄×#2132 #493015

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

Aliases

Subgroups

1384 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 400211);