This graph is the complement of the Johnson graph $\mathrm{J}(27,2)$.
| Number of vertices: | $351$ |
| Diameter: | $2$ |
| Intersection array: | $\{300,46;1,276\}$ |
| Spectrum: | $300^1 1^{324} (-24)^{26}$ |
| Automorphism group: | $\mathrm{S}_{27}$ |
| Distance-transitive: | Yes |
| Primitive |