The fairness of biometric systems, in particular facial recognition, is often analysed for larger demographic groups, e.g. female vs. male or black vs. white. In contrast to this, minority groups are commonly ignored. This paper investigates the performance of facial recognition algorithms on individuals with Down syndrome, a common chromosomal abnormality that affects approximately one in 1,000 births per year. To do so, a database of 98 individuals with Down syndrome, each represented by at least five facial images, is semi-automatically collected from YouTube. Subsequently, two facial image quality assessment algorithms and five recognition algorithms are evaluated on the newly collected database and on the public facial image databases CelebA and FRGCv2. The results show that the quality scores of facial images for individuals with Down syndrome are comparable to those of individuals without Down syndrome captured under similar conditions. Furthermore, it is observed that face recognition performance decreases significantly for individuals with Down syndrome, which is largely attributed to the increased likelihood of false matches.