Finite Group Databasebeta

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#10360⋊C₃ #11709149

• solvable
• stem

Aliases

Splittings

Subgroups

111 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

3,2^8|b^2=eh,c^2=e,f^2=h,g^2=hi,b^a=cegh,c^a=bcfhi,d^a=dg,e^a=ehi,f^a=g,g^a=fgi,h^a=hi,i^a=h,c^b=ce,d^b=df,f^b=fh,g^b=gi,d^c=dg,f^c=fi,g^c=ghi,f^d=fh,g^d=ghi

Conjugacy classes & character table

22 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 1083530);