Smith Equivalent Aut(A₆)-Representations Are Isomorphic

Many authors, e.g. M. Atiyah, R. Bott, J. Milnor, G. Bredon, S. Cappell, J. Shaneson, C. Sanchez, T. Petrie, E. Laitinen, K. Pawałowski, R. Solomon and so on, studied Smith equivalent representations for finite groups. Observing their results, E. Laitinen conjectured that nonisomorphic Smith equivalent real G-modules exist if $a_{G}$ , the number of real conjugacy classes of elements not of prime power order in G, is greater than or equal to 2. This paper shows that in the case G = Aut(A₆), $a_{G}=2$ any two Smith equivalent real G-modules are isomorphic.