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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

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    You might experiment first with, say, all the groups of order 16. Look at the order in which they appear in the various sources that list them, and see whether any make visual sense.2012-02-03
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    Nice question, I don't have an answer for! But I would like to see such a video after you have made one. Please share the link here with us after you have made the video!2012-02-03
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    It would, perhaps, make sense to put the abelian ones together, as a group is abelian if and only if it has symmetric group table. However, only a small fraction of groups of order $128$ are abelian!2012-02-03

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