Recently, Prasad and Yeung classified all possible fundamental groups of fake projective planes. According to their result, many fake projective planes admit a nontrivial group of automorphisms, and in that case it is isomorphic to , , 7:3 or , where 7:3 is the unique nonabelian group of order 21.
Let be a group of automorphisms of a fake projective plane . In this paper we classify all possible structures of the quotient surface and its minimal resolution.
"Quotients of fake projective planes." Geom. Topol. 12 (4) 2497 - 2515, 2008. https://doi.org/10.2140/gt.2008.12.2497