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D₄×#368 #497850

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

Aliases

Subgroups

622 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 36 points:

(1,2)(3,4);(2,4);(5,6,9,14,11,15,10,25)(7,16,19,31,21,32,20,35)(8,22,23,29,24,36,17,13)(12,26,27,34,28,33,30,18);(5,7,17,33,10,20,24,34,11,21,23,26,9,19,8,18)(6,12,22,31,14,27,29,32,15,28,36,35,25,30,13,16)

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, 405046);