How would I represent this on a cladogram?
The short answer is that cladograms are not compatible with Linnean taxonomy.

The longer answer explain how and why. First, there aren't enough ranks in Linnean taxonomy to cover all the cladogram nodes. The "kingdom-phylum-class-order-family..." was originally based on similiarity and not on phylogenetic relationship. For example: the class Reptilia is no longer a clade, and the class Aves is a subclade of the order Sauroschia (of the "super"-order Dinosauria, which is a clade of Diapsida which includes modern reptiles and crocodiles). The birds (Aves) are evolution descendants of dinosaurs but they ranked by Linneous as class while dinosaurs, according to Linnean taxonomy were at most super-order.

So you need to choose: a pseudo-Linnean relationship tree or a cladogram phylogenetic tree (and then you should omit the ranks' names "class", "order" etc.

I'll try to sketch the tree you described:


 A
 |
 |-- B
 |-- C
 |
 .
 .
 .