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D₄×#577 #10576139

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

Aliases

Subgroups

10609 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10483335);