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.