This is one of two self-complementary, rank-3 strongly-regular graphs with parameters $(81,40,19,20)$, the other being the Paley graph $P_{81}$.
| Number of vertices: | $81$ |
| Diameter: | $2$ |
| Intersection array: | $\{40,20;1,20\}$ |
| Spectrum: | $40^1 4^{40} (-5)^{40}$ |
| Automorphism group: | $3^4:\left(\mathrm{SL}(2,5):2^2\right)$ |
| Distance-transitive: | Yes |
| Primitive |