Automorphisms of Coverings of Strongly Regular Graphs with Parameters (81,20,1,6)

The possible orders and subgraphs of fixed points of the automorphisms of distance-regular graphs of diameter 4 which are $r$-coverings of a strongly regular graph with parameters (81,20,1,6) for $r\in\{2,3,6\}$ are found. It is proved that, if the automorphism group of a covering of the above type acts transitively on the set of vertices of the graph, then $r=3$.