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Q₈×#534 #7665726

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

Aliases

Subgroups

8668 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 20 points:

(1,2,3,4)(5,8,7,6);(1,5,3,7)(2,6,4,8);(10,12)(13,14)(15,19)(16,17)(18,20);(14,17)(18,19);(9,10)(11,12)(13,14)(15,18)(16,17)(19,20);(13,15)(14,18)(16,20)(17,19)

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, 7572922);