Is there an efficient way to look for all the characteristic subgroups of a group in GAP?
I'm only interested in finite groups.
The best I can do so far is collect all the normal subgroups into a list and check one-by-one if they are characteristic. Honestly, I haven't tried how slow this method is on finite groups of large orders, but feels like it should be quite slow.
Is there a smarter way?
What if we tighten our conditions and only look for certain characteristic subgroups for example characteristic cyclic subgroups or maybe even abelian ones?