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C₄×#3021 #6372707

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

Aliases

Subgroups

4719 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6279903);