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C₄×#2126 #493003

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

Aliases

Subgroups

1432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400199);