Two Nonisomorphic Groups of Order 96 with Isomorphic Tables of Marks and Noncorresponding Centres and Abelian Subgroups

摘要

We construct two nonisomorphic groups G and Q of order 96 which have isomorphic tables of marks, but such that the centre of G has order 8 and the centre of Q has order 4. We also note that G has an abelian subgroup of order 48, whereas Q has no abelian subgroup of that order. This also leads us to conclude that this isomorphism of tables of marks does not preserve normalizers.