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Q₈×#456 #6625575

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

Aliases

Subgroups

2876 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);(9,10,14,12)(11,17,20,24)(13,21,23,16)(15,22,18,19);(9,11)(10,15)(12,18)(13,22)(14,20)(16,24)(17,21)(19,23);(9,12,14,10)(11,18,20,15)(13,16,23,21)(17,22,24,19)

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, 6532771);