Erich writes: << [I wrote:]

But what if, for each n -- say 1 <= n <= 100, we ask specifically for the arrangement(s) of n points in the plane having the largest-size symmetry group?

why isn't the answer n equally spaced points on a circle?

...

This is clearly the right answer, and yet another confirmation that I tend to post too hastily. Sorry about that. Thus S_2(n) = 2n There are still many non-obvious questions in this area. What's the "best" arrangement(s) for the square torus T := R^2/Z^2 ? E.g., on T for n = 5 points, that tiling of T by 5 congruent squares gives an arrangement of 5 points -- the tiling's vertices -- whose full symmetry group is of order 20. Is there an arrangement of 5 points in T with a larger symmetry group? I suspect not. --Dan