It has degree 7, with 24 vertices and 84 edges.
It has girth 3, diameter 3 and radius 3.
Its symmetry group is PGL(2,7), with 336 elements.
It is not bipartite.
It is Hamiltonian.
It is symmetric.
It is 1-arc-transitive.
Its distance-list is 1,7,14,2.
https://en.wikipedia.org/wiki/Klein_graphs
7-valent Klein graph is the skeleton of the dual Klein map
For copyright details of Wikipedia image see Klein-graph-7-valent_Hamiltonian.svg.
