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D₄×#551 #7699478

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

Aliases

Subgroups

9171 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)(7,13,14,10)(9,11,16,18)(15,19,20,17);(5,7,9,15)(6,10,11,17)(8,14,16,20)(12,13,18,19);(6,11)(10,17)(12,18)(13,19);(7,14)(10,13)(15,20)(17,19)

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7606674);