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Q₈×#551 #7699651

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

Aliases

Subgroups

5705 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 24 points:

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

Conjugacy classes & character table

125 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7606847);