How can I find a non-abelian subgroup in this Cayley table? I tried all kinds of things, like $\{A,B,C,D,E,F,G,H\}$ or $\{A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W\}$, but they are all abelian. Maybe the trick is to get some blocks that are coloured together, but then I have to extend these blocks, and I just seem to get too many elements then.
Any ideas?
Notice that $oi=D$ and $io=F$. (I may have reversed these, not sure which order to read the table in. The important thing is they don't commute. Edit: fixed reversal) Can you figure out what the subgroup generated by $o$ and $i$ is? I.e. what is the subgroup $\langle o,i\rangle\le G$? Alternatively, find any subgroup containing both of them.