On finite induced crossed modules and the homotopy 2-type of mapping cones 
Ronald Brown and Christopher D. Wensley 

Abstract:
Results on the finiteness of induced crossed modules are proved both 
algebraically and topologically. Using the Van Kampen type theorem for the 
fundamental crossed module, applications are given to the 2-types of mapping 
cones of classifying spaces of groups. Calculations of the cohomology classes 
of some finite crossed modules are given, using crossed complex methods.