Large Language Models (LLMs) enhanced with Retrieval-Augmented Generation (RAG) have achieved substantial improvements in accuracy by grounding their responses in external documents that are relevant to the user's query. However, relatively little work has investigated the impact of RAG in terms of fairness. Particularly, it is not yet known if queries that are associated with certain groups within a fairness category systematically receive higher accuracy, or accuracy improvements in RAG systems compared to LLM-only, a phenomenon we refer to as query group fairness. In this work, we conduct extensive experiments to investigate the impact of three key factors on query group fairness in RAG, namely: Group exposure, i.e., the proportion of documents from each group appearing in the retrieved set, determined by the retriever; Group utility, i.e., the degree to which documents from each group contribute to improving answer accuracy, capturing retriever-generator interactions; and Group attribution, i.e., the extent to which the generator relies on documents from each group when producing responses. We examine group-level average accuracy and accuracy improvements disparities across four fairness categories using three datasets derived from the TREC 2022 Fair Ranking Track for two tasks: article generation and title generation. Our findings show that RAG systems suffer from the query group fairness problem and amplify disparities in terms of average accuracy across queries from different groups, compared to an LLM-only setting. Moreover, group utility, exposure, and attribution can exhibit strong positive or negative correlations with average accuracy or accuracy improvements of queries from that group, highlighting their important role in fair RAG. Our data and code are publicly available from Github.