It is below Phylum and above Order.
History of the concept
The class as a distinct rank of biological classification having its own distinctive name (and not just called a higher genus (genus summum)) was first introduced by a French botanist Joseph Pitton de Tournefort in his classification of plants (appeared in his 1694 Eléments de botanique). Carolus Linnaeus was the first to apply it consistently to the division of all three kingdoms of Nature (minerals, plants, and animals) in his Systema Naturae (1735, 1st. Ed.). Since then class had been considered the highest level of the taxonomic hierarchy until the embranchements, now called phyla, and divisions were introduced in the nineteenth century.