To confirm a diagnosis of high-grade B-cell lymphoma with double-hit (DH) or triple-hit (TH) features (HGBCL-DH/TH), the specific cytogenetic findings involve the rearrangement of key oncogenes, notably MYC, BCL2, and BCL6. The gene discussed is BCL6; the disease is B-cell non-Hodgkin lymphoma.