This graph is the complement of the Johnson graph $\mathrm{J}(39,2)$.
| Number of vertices: | $741$ |
| Diameter: | $2$ |
| Intersection array: | $\{666,70;1,630\}$ |
| Spectrum: | $666^1 1^{702} (-36)^{38}$ |
| Automorphism group: | $\mathrm{S}_{39}$ |
| Distance-transitive: | Yes |
| Primitive |