Understanding the organization and dynamics of social groups of marine mammals through the study of kin relationships is particularly challenging. Here, we studied a stable social group of sperm whales off Mauritius, using underwater observations, individual-specific identification, non-invasive sampling and genetic analyses based on mitochondrial sequencing and microsatellite profiling. Twenty-four sperm whales were sampled between 2017 and 2019. All individuals except one adult female shared the same mitochondrial DNA (mtDNA) haplotype—one that is rare in the western Indian Ocean—thus confirming with near certainty the matrilineality of the group. All probable first- and second-degree kin relationships were depicted in the sperm whale social group: 13 first-degree and 27 second-degree relationships were identified. Notably, we highlight the likely case of an unrelated female having been integrated into a social unit, in that she presented a distinct mtDNA haplotype and no close relationships with any members of the group. Investigating the possible matrilineality of sperm whale cultural units (i.e. vocal clans) is the next step in our research programme to elucidate and better apprehend the complex organization of sperm whale social groups.