This graph is the unique rank-3 $\mathrm{SRG}(253,112,36,60)$. It is a Cayley graph. The unique $\mathrm{SRG}(176,70,18,34)$ is an induced subgraph of this graph.
| Number of vertices: | $253$ |
| Diameter: | $2$ |
| Intersection array: | $\{112,75;1,60\}$ |
| Spectrum: | $112^1 2^{230} (-26)^{22}$ |
| Automorphism group: | $\mathrm{M}_{23}$ |
| Distance-transitive: | Yes |
| Primitive |