The actual muscle doing the work is the lateral rectus. It is one of the six extraocular muscles that move the eye.
It is unique because it is the only muscle controlled by the abducens nerve (CN VI). Abducens Nerve: What It Is, Function, Location & Conditions abducens muscle
To abduct the eye, which means rotating the gaze horizontally away from the midline of the body. The actual muscle doing the work is the lateral rectus