Advances in the understanding of developmental brain disorders such as autism spectrum disorders (ASD) is being achieved through human neurogenetics such as, for example, identifying de novo mutations in SYNGAP1 as one relatively common cause of ASD. A recently developed rat line lacking the calcium/lipid binding (C2) and GTPase activation protein (GAP) domain may further help uncover the neurobiological basis of deficits in children with ASD. This study focused on social dominance in the tube test using Syngap (rats heterozygous for the C2/GAP domain deletion) as alterations in social behaviour are a key facet of the human phenotype. Male animals of this line living together formed a stable intra-cage hierarchy, but they were submissive when living with WT cage-mates thereby modelling the social withdrawal seen in ASD. The study includes a detailed analysis of specific behaviours expressed in social interactions by WT and mutant animals, including the observation that when the Syngap mutants which had been living together had separate dominance encounters with WT animals from other cages, the two higher ranking Syngap rats remained dominant whereas the two lower ranking mutants were still submissive. While only observed in a small subset of animals, these findings support earlier observations with a rat model of Fragile-X indicating that their experience of winning or losing dominance encounters has a lasting influence on subsequent encounters with others. Our results highlight and model that even with single-gene mutations, dominance phenotypes reflect an interaction between genotypic and environmental factors.