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D₄×#454 #6573660

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

Aliases

Subgroups

4673 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6480856);