This graph is the complement of the Johnson graph $\mathrm{J}(24,2)$.
| Number of vertices: | $276$ |
| Diameter: | $2$ |
| Intersection array: | $\{231,40;1,210\}$ |
| Spectrum: | $231^1 1^{252} (-21)^{23}$ |
| Automorphism group: | $\mathrm{S}_{24}$ |
| Distance-transitive: | Yes |
| Primitive |