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Let G be a group and M(q) be one of the Lie type simple groups 2Dn(q) (n ≥ 4) and Dn(q) (n odd, n ≥ 5). In this paper, we prove that G ≌ M(q)if and only if (I) πe(G) = πe(M(q)), where πe(G) is the set of orders of elements in G; and (ii) |G| = |M(q)|.