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Q₈×#454 #6625571

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

Aliases

Subgroups

2891 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);(10,14)(12,19)(15,23)(16,20)(17,21)(22,24);(9,10)(11,15)(12,20)(13,16)(14,19)(17,22)(18,24)(21,23);(9,11,13,18)(10,15,16,24)(12,21,19,17)(14,22,20,23)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6532767);