Bacterial diversity can be overwhelming. There is an ever-expanding number of bacterial taxa being discovered, but many of these taxa remain uncharacterized with unknown traits and environmental preferences. This diversity makes it challenging to interpret ecological patterns in microbiomes and understand why individual taxa, or assemblages, may vary across space and time. While we can use information from the rapidly growing databases of bacterial genomes to infer traits, we still need an approach to organize what we know, or think we know, about bacterial taxa to match taxonomic and phylogenetic information to trait inferences. Inspired by the periodic table of the elements, we have constructed a \'periodic table\' of bacterial taxa to organize and visualize monophyletic groups of bacteria based on the distributions of key traits predicted from genomic data. By analyzing 50,745 genomes across 31 bacterial phyla, we used the Haar-like wavelet transformation, a model-free transformation of trait data, to identify clades of bacteria which are nearly uniform with respect to six selected traits - oxygen tolerance, autotrophy, chlorophototrophy, maximum potential growth rate, GC content and genome size. The identified functionally uniform clades of bacteria are presented in a concise \'periodic table\'-like format to facilitate identification and exploration of bacterial lineages in trait space. While our approach could be improved and expanded in the future, we demonstrate its utility for integrating phylogenetic information with genome-derived trait values to improve our understanding of the bacterial diversity found in environmental and host-associated microbiomes.