Rich subgroups in groups of order up to 2000

This file contains information about nontrivial rich subgroups in groups G of order up to 2000, i. e., subgroups H with the property that the restriction of each character of G to H has a trivial constituent. Rich subgroups are studied in the paper On Frobenius graphs of diameter 3 for finite groups. The DOI for the data file is 10.5281/zenodo.12731413. The contents of the file is an array of length 3.

• The first entry is this description, an array of strings.
• The second entry is an array that lists the isomorphism types of the groups G; each entry has the format `[[n,i],[m1,m2,...,mk]]` meaning that G can be obtained as i-th group of order n in the small groups library, and the representatives of the k conjugacy classes of rich subgroups in G have orders |m1|, |m2|, ..., |mk|; mj is positive if the j-th class of rich subgroups consists of diameter three subgroups of G, and negative otherwise.
• The third entry is an array that lists the isomorphism types of those groups G that are minimal w.r.t. inclusion with the property that they contain a rich subgroup; each entry has the format `[[n1,i1],[n2,i2],...,[nk,ik]]` meaning that the i1-th group of order n1, the i2-th group of order n2, ..., the ik-th group of order nk are minimal and that they are isoclinic.