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D₄×#553 #7699480

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

Aliases

Subgroups

8489 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)(7,8)(9,10)(11,12)(14,17)(18,19);(6,10)(8,11)(13,14,16,17)(15,19,20,18);(5,7)(6,11)(8,10)(9,12);(5,8,9,11)(6,7,10,12)(13,15,16,20)(14,18,17,19)

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, 7606676);