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D₄×#350 #497273

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

Aliases

Subgroups

1107 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 404469);