I am poking at reproducing some fundamental research in group theory. In particular, I want to reproduce the OEIS sequence #1. The crux of the problem is not generating potential groups, this can be accomplished by a sat-solver and about 20 lines of code, but determining which of those groups so generated are isomorphic.
The finite group isomorphism algorithms are tractable, but computationally a bit hairy, so I am keen to determine what heuristics can be employed to save some compute on clearly not isomorphic groups. A few obvious examples are:
- Groups with different order
- Groups with different Caylee skeleton (number of non-self identity elements)
In short, I would love some form or precomputation or fingerprint that I can compute to avoid comparing obviously different groups.