A performance gap between the genders has been observed on the Force Concept Inventory (FCI) almost since its introduction. Many studies have sought to characterize this gender gap, however, few have tested the consistency of the factor structure across the genders. This study fills in this gap by offering the first piece of evidence that the genders (male and female due to data constraints) are interacting with the FCI in similar manners. Using multigroup measurement invariance techniques, a preinstruction sample of 6238 males and 2874 females, and a postinstruction sample of 6338 males and 2955 females, the latent variable structure of the FCI was tested for consistency between the genders. As this technique is not often used by the physics education research community, significant time was spent explaining the methodology. It was found that the Eaton and Willoughby five-factor modified (EW5M) model of the FCI factor structure exhibited strict invariance between the genders. Additionally, a single-factor model showed strong invariance and partial strict invariance for the FCI. Latent means from the EW5M model revealed that females underperform compared to males across all of the factors of the FCI, but these gaps in performance decreased over the course of instruction, however, some differences are still large. The results of this study suggest observed performance differences on the FCI between the genders may not be due to gender specific factor structure differences. However, this result is sample dependent and should be verified by other studies using different, independent samples.