Quandles can be regarded as generalizations of symmetric spaces. Among symmetric spaces, two-point homogeneous Riemannian manifolds would be the most fundamental ones. In this paper, we define two-point homogeneous quandles analogously, and classify those with prime cardinality.
"Two-point homogeneous quandles with prime cardinality." J. Math. Soc. Japan 65 (4) 1117 - 1134, October, 2013. https://doi.org/10.2969/jmsj/06541117