Every finite non-abelian group admits a non-Cayley Haar graph, except the dihedral groups of orders 6, 8, and 10, the quaternion group Q8, and Q8 × Z2.
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Existence of non-Cayley Haar graphs
Every finite non-abelian group admits a non-Cayley Haar graph, except the dihedral groups of orders 6, 8, and 10, the quaternion group Q8, and Q8 × Z2.