Some individuals with autism find it challenging to use and understand language in conversation, despite having good abilities in core aspects of language such as grammar and vocabulary. This suggests that pragmatic skills (such as understanding implied meanings in conversation) are separable from core language skills. However, it has been surprisingly difficult to demonstrate this dissociation in the general population. We propose that this may be because prior studies have used tasks in which different aspects of language are confounded. The present study used novel language tasks and factor analysis to test whether pragmatic understanding of implied meaning, as part of a broader domain involving social understanding, is separable from core language skills. 120 adult participants were recruited online to complete a 7-task battery, including a test assessing comprehension of conversational implicature. In confirmatory analysis of a preregistered model, we compared whether the data showed better fit to a two-factor structure (including a "social understanding" and "core language" factor) or a simpler one-factor structure (comprising a general factor). The two-factor model showed significantly better fit. This study supports the view that interpreting context-dependent conversational meaning is partially distinct from core language skills. This has implications for understanding the pragmatic language impairments reported in autism.