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Q₈×#538 #7665627

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

Aliases

Subgroups

5638 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)(11,17)(12,16)(13,15)(14,18)(19,21)(20,23)(22,24);(9,11,13,19)(10,14,15,22)(12,18,20,24)(16,17,23,21);(10,15)(11,18)(14,21)(16,23)(17,22)(19,24);(10,16)(14,17)(15,23)(21,22)

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, 7572823);