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C₂²×#551 #62703

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

Aliases

Subgroups

4763 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

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

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, 55691);