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D₄×#135 #61048

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

Aliases

Subgroups

1411 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 54036);