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Q₈×#509 #7623925

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

Aliases

Subgroups

1364 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);(9,10)(11,14)(12,21)(13,15)(16,18)(17,19)(20,22)(23,24);(10,14)(11,18)(12,19)(15,22)(16,17)(20,24)(21,23);(10,15)(14,22)(16,23)(17,21)

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, 7531121);