I am currently doing some calculations with the larger sporadic groups (matrix
representations) and need to be able to compute centralizers. This proves
impossible in a variety of cases.
However, I am not utilising the fact that I know the centralizer sizes from the
ATLAS. I believe it may be advantageous for me to find an element which
commutes with my given one, find the order of the subgroups they generate,and
keep doing this ... until the subgroup reaches the desired size.
To implement this I need to know the centralizer algorithm (for matrix groups).
Does anyone know it? Any other ideas?