How loss of genetic exchanges (recombination) evolves between sex chromosomes is a long‐standing question. Suppressed recombination may evolve when a sexually antagonistic (SA) polymorphism occurs in a partially sex‐linked ‘pseudoautosomal’ region (or ‘PAR’), maintaining allele frequency differences between the two sexes, and creating selection for closer linkage with the fully sex‐linked region of the Y chromosome in XY systems, or the W in ZW sex chromosome systems. Most evidence consistent with the SA polymorphism hypothesis is currently indirect, and more studies of the genetics and population genetics of PAR genes are clearly needed. The sex chromosomes of the plant Silene latifolia are suitable for such studies, as they evolved recently and the loss of recombination could still be ongoing. Here, we used RAD sequencing to genetically map sequences in this plant, which has a large genome (c. 3 gigabases) and no available whole‐genome sequence. We mapped 83 genes on the sex chromosomes, and comparative mapping in the related species S. vulgaris supports previous evidence for additions to an ancestral PAR and identified at least 12 PAR genes. We describe evidence that recombination rates have been reduced in meiosis of both sexes, and differences in recombination between S. latifolia families suggest ongoing recombination suppression. Large allele frequency differences between the sexes were found at several loci closely linked to the PAR boundary, and genes in different regions of the PAR showed striking sequence diversity patterns that help illuminate the evolution of the PAR.