Characterizability of the group 2D p(3) by its order components, where p ≥ 5 is a prime number not of the form 2m+1

The author will prove that the group (2)D (p) (3) can be uniquely determined by its order components, where p not equal 2(m) + 1 is a prime number, p >= 5. More precisely, if OC(G) denotes the set of order components of G, we will prove OC(G) = OC((2)D(p) (3)) if and only if G is isomorphic to (2)D(p) (3). A main consequence of our result is the validity of Thompson's conjecture for the groups under consideration.