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Q₈×#393 #4307448

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

Aliases

Subgroups

4474 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 24 points:

(1,2,3,4)(5,8,7,6);(1,5,3,7)(2,6,4,8);(14,16)(17,18,20,22)(19,23,24,21);(10,12)(14,16)(17,19,20,24)(18,21,22,23);(9,10)(11,12)(13,14)(15,16)(17,18)(19,23)(20,22)(21,24)

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, 4214644);