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Q₈×#575 #10576218

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

Aliases

Subgroups

6447 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)(11,18)(12,17)(13,21)(14,16)(15,19)(20,24)(22,23);(9,11)(10,15)(12,19)(13,22)(14,20)(16,23)(17,24)(18,21);(10,16)(15,23)(17,21)(18,24);(9,12,14,13)(10,17,16,21)(11,19,20,22)(15,24,23,18)

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, 10483414);