SnAn naming algorithm #348
Description
Related to #265. We included code from magma to guess the degree of a potentially alternating or symmetric group. However, this code tests a lot of element orders and creates a lot of overhead. In particular, it does not recognise for many groups that they cannot be Sn or An. @aniemeyer suggested that we could improve on this method by first determining a lower bound for the degree n (like in magma) but with far fewer tries, then taking this initial guess and check if elements of order close to n (n-cycles) can be found in e.g. 2n tries. We might need to revise n upwards after these trials. It is also worth looking into FindHomMethodsProjective.AltSymBBByDegree if something in this code is already attempting to guess the degree.