Mr. Isaacs was Sibyl Vane's manager and producer of the theatre. He is described as "fat" and "stereotypically Jewish". Mr. Isaacs greets Gray at the door to the theatre and takes them to their box seats.
Dorian despises Mr. Isaacs. Their relationship was strained at best. At one point in the story, Dorian refers to Isaacs as a Caliban. (A caliban is not man - not beast and is described as evil, crude, but not vulgar in Shakespeare's The Tempest.)