This website provides code to support the calculations in the paper Simultaneous conjugacy classes as combinatorial invariants of finite groups. The main computations of the article are summarized in Table 1 in the article. These formulas can be validated by cross-checking against explicit calculations in GAP using its small groups library.
Each line of the file normalized_invariants.txt is of the form (str, a, b), where str is a string describing an isoclinism family, and a and b are the normalized generating functions AG(t/|G|) and BG(t/|G|).
Each line of the file small_groups_in_isoclinism_families.txt is of the form (str,list) where str is a string describing an isoclinism family, and list is a list of id's in the GAP small groups library of groups in that family.
As in Table 1 of the article, some classes of 2-groups are merged with classes of p-groups of p odd.
The file code_and_verification.ipynb is a jupyter worksheet running on a Sage kernel where the verification of formulae in Table 1 is carried out. This worksheet uses the two data files mentioned earlier. An html version of this worksheet is also available (for viewing the code without using it). One may use this code to compute the functions AG(t) and BG(t) for any GAP group.