How to construct a Cayley Table?

Question

I have a set G = {e,a,b,c,d,f,g,h,i,j,k,l,m,n,o,p} which forms a group, (G, *) which is shown in the Cayley Digraph below.

How do I go about constructing a Cayley table of (G,*), assuming e is the identity.

All I have so far is:

\begin{array}{|c|c|c|c|} \hline &e&a& b&c&d&f&g&h&i&j&k&l&m&n&o & p \\ \hline a& & &\\ \hline b& & &\\ \hline c& c&j&g&f&n&k&i&b&h&p&e&m&d&l&a&o\\ \hline d& d&b&a&n&e&l&j&o&p&g&m&f&k&c&h&i \\ \hline f& & &\\ \hline g& & &\\ \hline h& & &\\ \hline i& i&l&f&g&p&b&c&k&e&n&h&a&o&j&m&d\\ \hline j& & &\\ \hline k& & &\\ \hline l& & &\\ \hline m& & &\\ \hline n& & &\\ \hline o& & &\\ \hline p& & &\\ \end{array}

I don't think this is correct & have completely confused myself, any help and support would be much appreciated.

Answer 1

Looks good so far.... Try k next. Follow the same rule as c but follow the arrows backwards.

And f = c^2, takes everything across the black diamonds. P takes everything across the red/blue squares.
Then it starts getting trickier.

n = dc, na = d(ca) = dj = g.