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D₄×#568 #10574208

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

Aliases

Subgroups

10589 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

170 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10481404);