My final Cayley table for the dihedral group $D_6$. Does it look even remotely right? (Sorry to interrupt the flow of conversation).

$$\begin{array}{c|c|c|c|c|c|c|c|c|c|c|c|c|}
\circ & e & r & r^2& r^3& r^4& r^5& f& rf& r^2f& r^3f& r^{4}f& r^{5}f \\
\hline e & e & r & r^2& r^3& r^4& r^5& f& rf& r^2f& r^3f& r^{4}f& r^{5}f \\
\hline r & r & r^2 & r^3 & r ^4 & r ^5 & e & rf & r^2f & r^3f & r^4f & r^5f & f\\
\hline r^2 & r^2 & r^3 & r ^4 & r ^5 & e & r & r^2f & r^3f & r^4f & r^5f & f & rf\\
\hline r^3& r^3 & r ^4 & r ^5 & e & r & r^2 & r^3f & r^4f & r^5f & f & rf & r^2f\\