TITLE: linearly arranging the group tables of groups of order 128
QUESTION [5 upvotes]: I'm planning to make a video that shows color coded group tables for all 2328 groups of order 128 -- at 128$\times$128 pixels at 24 frames a second I think I get 97 seconds of video. Is there some logical order that the all these groups can be placed in that would make the most visual sense? 
It's done! Here: http://www.youtube.com/watch?v=25Qzu-KuVs4

REPLY [3 votes]: I would be inclined to follow the ordering in the GAP/Magma libraries, which sorts first by number of generators. So you get the cyclic group (tall and thin) first and the elementary abelian group (short and wide) last. Of course the huge majority of the groups have 3,4 or 5 generators.
Groups with the same generator number are sorted in ascending order of exponent $p$-class (which is similar to but not quite the same as nilpotency class).  But again you get huge numbers of group with, for example, 4 generators and class 2, which are all very similar to each other. So perhaps the video should go slowly at the beginning and end, when group properties are changing more rapidly, and speed up during the repetitive middle sections!