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C₄×#547 #34159

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

Aliases

Subgroups

1634 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 16 points:

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

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, 27147);