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D₄×#554 #7699477

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

Aliases

Subgroups

8135 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7606673);