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C₂²×#542 #62678

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

Aliases

Subgroups

3987 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)(7,11)(8,10)(9,12)(15,19)(17,20);(5,6,8,10)(7,9,12,11)(13,14,16,18)(15,17,19,20);(5,6)(7,9)(8,10)(11,12)(13,15)(14,17)(16,19)(18,20);(5,7,8,12)(6,9,10,11)

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 55666);