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D₄×#458 #6573712

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

Aliases

Subgroups

5088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 6480908);