This graph is the unique rank-3 strongly regular graph with parameters $(36,14,4,6)$. This graph is also known as the $\mathrm{U}_3(3)$ graph. This graph is a member of the Suzuki tower. It is the first subconstituent of the Hall–Janko graph. The first subconstituent of this graph is the distance-3 graph of the Heawood graph. This graph is uniquely determined by its strongly regular graph parameters and 2-rank.
| Number of vertices: | $36$ |
| Diameter: | $2$ |
| Intersection array: | $\{14,9;1,6\}$ |
| Spectrum: | $14^1 2^{21} (-4)^{14}$ |
| Automorphism group: | $\mathrm{G}_2(2) \cong \mathrm{PSU}(3,3):2 \cong \mathrm{P} \Gamma \mathrm{U}(3,3)$ |
| Distance-transitive: | Yes |
| Primitive |