Commutative hypergroups of order 5 and constant length 2

In an earlier paper [Istit. Lombardo Accad. Sci. Lett. Rend. A 120 (1986), 41--56; MR0927867 (89e:20129)] the author defined hypergroups of constant length n as hypergroups in which |xy|=n for all x,y∈H , and he studied hypergroups of constant length 2 and orders 3 and 4. In this paper he determines all commutative hypergroups of constant length 2 and order 5 properly containing the core; he also describes a computer program to check associativity.