I think this will almost do what you want.
[~,~,bin_numbers] = histcounts(diameters,edges);
The output bin_numbers will show, for each diameter, which bin it falls into (what I think you are calling 'class') in your original question. Then, for example, diameters(bin_numbers==1) will be a vector of all of the diameters in the first bin.
In general there might be different numbers of diameters in the different bins, so you might not be able to format the data into a 2d matrix like you show above (i.e., different rows would need different numbers of columns).