There is a growing body of gender studies in software engineering to understand diversity and inclusion issues, as diversity is recognized to be a key issue to healthy teams and communities. A second factor often linked to team performance is personality, which has received far more attention. Very few studies, however, have focused on the intersection of these two fields. Hence, we set out to study gender differences in personality traits of software engineers. Through a survey study we collected personality data, using the HEXACO model, of 483 software engineers. The data were analyzed using a Bayesian independent sample t-test and network analysis. The results suggest that women score significantly higher in Openness to Experience, Honesty-Humility, and Emotionality than men. Further, men show higher psychopathic traits than women. Based on these findings, we develop a number of propositions that can guide future research.