mjo@gentoo.org frp.bissey@gmail.com François Bissey proxy-maint@gentoo.org Proxy Maintainers sci-mathematics@gentoo.org Gentoo Mathematics Project The concept of a table of marks was introduced by W. Burnside in his 1955 book Theory of Groups of Finite Order. Therefore a table of marks is sometimes called a Burnside matrix. The table of marks of a finite group G is a matrix whose rows and columns are labelled by the conjugacy classes of subgroups of G and where for two subgroups H and K the (H, K)-entry is the number of fixed points of K in the transitive action of G on the cosets of H in G. So the table of marks characterizes the set of all permutation representations of G. Moreover, the table of marks gives a compact description of the subgroup lattice of G, since from the numbers of fixed points the numbers of conjugates of a subgroup K contained in a subgroup H can be derived. For small groups the table of marks of G can be constructed directly in GAP by first computing the entire subgroup lattice of G. However, for larger groups this method is unfeasible. The GAP Table of Marks library provides access to several hundred tables of marks and their maximal subgroups. gap-packages/tomlib