Which class of animals constitute the largest biomass?
Following from MarchHo's comment, I have not been able to find class-specific (in the formal sense) estimates, but if you meant 'class' in an informal sense, the following may be useful.

A nice infographic covering the relative biomass of all land mammals is here, and a full table for species groups (at the level of domesticated vertebrates, invertebrates, etc) is here (reproduced below).



Short answer: amongst animals, invertebrates are where the mass is.