DETERMINATION OF THE UNISERIAL SPACE GROUPS WITH A GIVEN COCLASS

The uniserial p-adic space groups of coclass r play a central role in the classification of the finite p-groups of coclass r. A practical algorithm to determine up to isomorphism the uniserial p-adic space groups of coclass r, where p is an odd prime, is described. As an application, these groups are constructed or counted for some values on p and r. For example, it is observed that there are 137 299 953 383 uniserial 3-adic space groups of coclass 4.