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Q₈×C₂²⋊Q₈ #36542

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

Aliases

Subgroups

1200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 20 points:

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 29530);