The concept of interaction classes (iClasses) for multi-environment trial data was introduced to address the problem of summarising variety performance across environments in the presence of variety by environment interaction (VEI). The approach involves the fitting of a factor analytic linear mixed model (FALMM), with the resultant estimates of factor loadings being used to form groups of environments (iClasses) that discriminate varieties with different patterns of VEI. It is then meaningful to summarise variety performance across environments within iClasses. The iClass methodology was developed with respect to a FALMM in which the genetic effects for different varieties were assumed independent. This was done for pedagogical reasons but it was pointed out that the accuracy of variety selection is greatly enhanced by considering the genetic relatedness of varieties, either via ancestral or genomic information. The focus of the current paper is therefore to extend the iClass approach for FALMMs which incorporate such information. In addition a measure of stability of variety performance across iClasses is defined. The utility of the approach for variety selection is illustrated using a multi-environment trial dataset from the lentil breeding program operated by Agriculture Victoria.