We consider the generalized Calogero–Moser–Sutherland quantum Hamiltonian H associated with a configuration of vectors AG2 on the plane which is a union of A2 and G2 root systems. The Hamiltonian H depends on one parameter. We find an intertwining operator between H and the Calogero–Moser–Sutherland Hamiltonian for the root system G2. This gives a quantum integral for H of order 6 in an explicit form, thus establishing integrability of H.

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