This graph is the unique rank-3 strongly regular graph with parameters $(36,15,6,6)$. The local graph of this graph is the Kneser graph $\mathrm{K}(6,2)$. The second subconstituent of this graph is the Johnson graph $\mathrm{J}(6,3)$. This graph is the local graph of the $\mathrm{NO}_6^+(3)$ graph. This graph is the second subconstituent of the $\mathrm{VO}_6^-(2)$ graph.
| Number of vertices: | $36$ |
| Diameter: | $2$ |
| Intersection array: | $\{15,8;1,6\}$ |
| Spectrum: | $15^1 3^{15} (-3)^{20}$ |
| Automorphism group: | $\mathrm{O}_5(3):2 \cong \mathrm{PS_p}(4,3):2$ |
| Distance-transitive: | Yes |
| Primitive |