Hi,
i need help with drawing up a cayley table for an octagon.
I presume you mean the Cayley table for the group of symmetries for a regular octagon.
First, how many elements are there in that group? There are the 8 rotations, of course, but then, since 8 is even, every line connecting two opposite vertices is a line of symmetry and every line bisecting a side is a line of symmetry. There are 4 pairs of opposite vertices and 4 pairs of parallel sides so there are a total of 8+ 4+ 4= 16 elements in this group and so [tex]16^2= 256 entries in the table.
I recommend drawing a picture, carefully labeling each of the 16 symmetries and then working very carefully!