This is one of two self-complementary, rank-3 strongly-regular graphs with parameters $(729,364,181,182)$, the other being the Paley graph $P_{729}$.
| Number of vertices: | $729$ |
| Diameter: | $2$ |
| Intersection array: | $\{364,182;1,182\}$ |
| Spectrum: | $364^1 13^{364} (-14)^{364}$ |
| Automorphism group: | $3^6:182:6$ |
| Distance-transitive: | Yes |
| Primitive |