Classifying 2-groups by coclass
Trans. Amer. Math. Soc. 351 (1999), 131-169. 

M. F. Newman 
School of Mathematical Sciences, Australian National University, Canberra, 
ACT 0200, Australia 
and 
E. A. O'Brien
Department of Mathematics, University of Auckland, Private Bag 92019, 
Auckland, New Zealand 

Abstract. Now that the conjectures of Leedham-Green and Newman have been 
proved, we probe deeper into the classification of $p$-groups using coclass. 
We determine the pro-$2$-groups of coclass at most $3$ and use these to 
classify the $2$-groups of coclass at most $3$ into families. Using extensive 
computational evidence, we make some detailed conjectures about the structure 
of these families. We also conjecture that the $2$-groups of arbitrary fixed 
coclass exhibit similar behaviour.