Finite Group Databasebeta

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#6860⋊Q₈ #14516107

• supersolvable
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^3,3^5|a^2=c,b^2=c,d^3=h^2,e^3=h^2,b^a=bc,d^a=d^2h,e^a=e^2h,f^a=fg^2h^2,g^a=g^2,h^a=h^2,e^d=ef,f^d=fh,f^e=fg

Conjugacy classes & character table

79 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 501);