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C₄×#556 #34166

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

Aliases

Subgroups

1170 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 27154);