Symmetry classes of mappings
The first group of programs is an application of the Cauchy-Frobenius Lemma
to group actions on the domain, the range and both on the domain and range.
For each permutation of the acting group the cycle type is evaluated, for that
reason the programs are rather slow.
Applying the Cauchy Frobenius Lemma which uses conjugacy classes of the acting
group, makes the programs much faster.