Finite Group Databasebeta

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#10319⋊C₃ #11709145

• solvable
• stem

Aliases

Splittings

Subgroups

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3,2^8|b^2=i,c^2=h,d^2=hi,e^2=h,f^2=i,g^2=hi,b^a=cefgh,c^a=dfh,d^a=bfg,e^a=gi,f^a=e,g^a=fh,h^a=hi,i^a=h,c^b=ce,d^b=df,e^b=eh,f^b=fi,g^b=ghi,d^c=dg,e^c=eh,f^c=fi,g^c=ghi,e^d=eh,f^d=fi,g^d=ghi

Conjugacy classes & character table

28 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083526);