Composition Factors from the Table of Marks

Let B(G) be the Burnside ring for a finite group G and let T(G) be the table of marks of G. It is known that, in general, neither B(G) nor T(G) determines the finite group G. That is, one can easily construct pairs of non-isomorphic finite groups such that their table of marks is the same (hence, their Burnside rings are isomorphic). In this note, we show that the composition factors of G are determined by the table of marks T(G).