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C₄×#443 #20509

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

Aliases

Subgroups

523 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 13497);