It is known that the so called pseudoarc can be represented as a quotient of a zero dimensional compact ”prespace” under an appropriate equivalence relation due to Irwin-Solecki (which is an inverse limit of linear graphs), and the automorphisms of this prespace densely embeds into the homeomorphism group of the pseudoarc. Although this embedding is only continuous, not a homeomorphic embedding, we can actually characterize the topology inherited from the homeomorphism group intrinsically, only in terms of the prespace. Using this characterization we prove that not all homeomorphisms are conjugate to an automorphism. Moreover, we generalize theorems of Kechris-Rosendal to characterize when the homeomorphism group of such a continuum (i.e. one that can be represented via a prespace) admits a dense or comeager conjugacy class, and we improve a theorem of Bice-Malicki showing that the diagonal action of the homeomorphisms of the pseudoarc on its countable product admits a dense conjugacy class. Joint with Slawomir Solecki.