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D₄×#538 #7664571

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

Aliases

Subgroups

9226 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)(7,13)(8,12)(9,11)(10,14)(15,17)(16,19)(18,20);(5,7,9,15)(6,10,11,18)(8,14,16,20)(12,13,19,17);(6,11)(7,14)(10,17)(12,19)(13,18)(15,20);(6,12)(10,13)(11,19)(17,18)

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, 7571767);