Dependency between orbits

Hi,

I'm struggling with the following:

I have a colored graph, and I used Bliss to find the generators group for the automorphisms. Finding the orbits given the generators is easy.

What I'm trying to find now is dependence between orbits - for each orbit I want to know if it still exist if I"ll stabilize the rest of the graph, and if not, which of the other orbits need to be "free" to move with it.

I tried searching in the computational group theory literature without success, but I may be missing some terminology here, any help will be appreciated.

Thanks!