Transcription factor that represses the transcription of a wide range of genes involved in cell proliferation and differentiation (PubMed:15337766, PubMed:15662416, PubMed:17495164, PubMed:26816381, PubMed:29813070). Directly and specifically binds to the consensus sequence 5'-[GA][CA]GACCCCCCCCC-3' and represses transcription both by regulating the organization of chromatin and through the direct recruitment of transcription factors to gene regulatory regions (PubMed:15337766, PubMed:15662416, PubMed:26816381, PubMed:29813070). Negatively regulates SMAD4 transcriptional activity in the TGF-beta signaling pathway through these two mechanisms (By similarity). That is, recruits the chromatin regulator HDAC1 to the SMAD4-DNA complex and in parallel prevents the recruitment of the transcriptional activators CREBBP and EP300 (By similarity). Collaborates with transcription factors like RELA to modify the accessibility of gene transcription regulatory regions to secondary transcription factors (PubMed:29813070). Also directly interacts with transcription factors like SP1 to prevent their binding to DNA (By similarity). Functions as an androgen receptor/AR transcriptional corepressor by recruiting NCOR1 and NCOR2 to the androgen response elements/ARE on target genes (By similarity). Thereby, negatively regulates androgen receptor signaling and androgen-induced cell proliferation (By similarity). Involved in the switch between fetal and adult globin expression during erythroid cells maturation (PubMed:26816381). Through its interaction with the NuRD complex regulates chromatin at the fetal globin genes to repress their transcription (PubMed:26816381). Specifically represses the transcription of the tumor suppressor ARF isoform from the CDKN2A gene (PubMed:15662416). Efficiently abrogates E2F1-dependent CDKN2A transactivation (PubMed:15662416). Regulates chondrogenesis through the transcriptional repression of specific genes via a mechanism that also requires histone deacetylation (PubMed:15337766). Regulates cell proliferation through the transcriptional regulation of genes involved in glycolysis (By similarity). Involved in adipogenesis through the regulation of genes involved in adipocyte differentiation (By similarity). Plays a key role in the differentiation of lymphoid progenitors into B and T lineages (PubMed:17495164). Promotes differentiation towards the B lineage by inhibiting the T-cell instructive Notch signaling pathway through the specific transcriptional repression of Notch downstream target genes (PubMed:17495164). Also regulates osteoclast differentiation (By similarity). May also play a role, independently of its transcriptional activity, in double-strand break repair via classical non-homologous end joining/cNHEJ (PubMed:26446488). Recruited to double-strand break sites on damage DNA, interacts with the DNA-dependent protein kinase complex and directly regulates its stability and activity in DNA repair (PubMed:26446488). May also modulate the splicing activity of KHDRBS1 toward BCL2L1 in a mechanism which is histone deacetylase-dependent and thereby negatively regulates the pro-apoptotic effect of KHDRBS1 (By similarity). Homodimer (By similarity). Interacts with BCL6 (PubMed:9927193). Interacts with RELA; involved in the control by RELA of the accessibility of target gene promoters (PubMed:29813070). Interacts with AR (via NR LBD domain); the interaction is direct and androgen-dependent (By similarity). Interacts with NCOR1 (By similarity). Interacts with NCOR2 (By similarity). Interacts with SMAD4; the interaction is direct and stimulated by TGFB1 (By similarity). Interacts with HDAC1 (By similarity). Interacts with SP1; ZBTB7A prevents the binding to GC-rich motifs in promoters and represses the transcriptional activity of SP1 (By similarity). Interacts with the DNA-dependent protein kinase complex/DNA-PKc (PubMed:26446488). Interacts with KHDRBS1; negatively regulates KHDRBS1 splicing activity (By similarity). Recruited to double-strand break sites of damaged DNA. Widely expressed (PubMed:9927193). In normal thymus, expressed in medullary epithelial cells and Hassle's corpuscles (at protein level) (PubMed:15662416). In the spleen, mainly expressed in the white pulp germinal centers (at protein level) (PubMed:15662416). Up-regulated in thymic lymphomas (PubMed:15662416). Expressed at 9.5-10.0 dpc in limb buds, pharyngeal arches, tail bud, placenta and neural tube (PubMed:9927193). Up-regulated during adipocyte differentiation (PubMed:14701838). The BTB domain mediates the interaction with the androgen receptor/AR and HDAC1. Also mediates the interaction with SP1. Sumoylated. Undergoes sumoylation with SUMO1 that may regulate its transcriptional activity. Death around 16.5 dpc because of severe anemia with a profound block in early B-cell development (PubMed:17495164). Conditional knockout in erythroid cells, leads to the expression of fetal globin in peripheral blood of adult mice and inefficient erythroid terminal differentiation (PubMed:26816381).