This graph is an induced subgraph of the distance-2 graph of the line graph of the Hoffman–Singleton graph. It is the unique strongly regular graph with parameters $(126,50,13,24)$ (as shown by Coolsaet and Degraer).
Its automorphism group is $\mathrm{S}_7$ acting transitively but imprimitively with rank 7.| Number of vertices: | $126$ |
| Diameter: | $2$ |
| Intersection array: | $\{50,36;1,24\}$ |
| Spectrum: | $50^1 2^{105} (-13)^{20}$ |
| Automorphism group: | $\mathrm{S}_7$ |
| Distance-transitive: | No |
| Primitive |