  The Prime Graph Question for integral group rings asks if it is true that if
the normalized unit group of the integral group ring of a finite group $G$
contains an element of order $pq$, for some primes $p$ and $q$, also $G$
contains an element of that order. We answer this question for the three Conway
sporadic simple groups after reducing it to a combinatorial question about
Young tableaus and Littlewood-Richardson coefficients. This finishes work of V.
Bovdi, A. Konovalov and S. Linton.
