Counting crystallographic groups in low dimensions

We present the results of our computations concerning the space groups of d imension 5 and 6. We find 222 018 and 28 927 922 isomorphism types of these groups, respectively. Some overall statistics on the number of Q-classes a nd Z-classes in dimensions up to six are provided. The computations were do ne with the package CARAT, which can parametrize, construct and identify al l crystallographic groups up to dimension 6.