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C₄×#3068 #6372914

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

Aliases

Subgroups

2739 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280110);