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There are various online resources for the classification of groups of small order, such as this one or that one.

Is there any nice reference in the literature which contains such a classification (say, for orders up to $30$, EDIT: $100$) with detailed proofs? It should only serve as a citation.

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I have thought that classifying small order groups is a routine task and can be used just as you'd use any other routine tools. So, sometimes I see that they are used without proof. But, I cannot find a paper, where, say classification of groups of order 24 is without proof. +1, indeed a nice question. – user21436 May 8 '12 at 8:15
I think several books contain a classification of all groups of order less than 60. See also – lhf May 8 '12 at 10:53
up vote 2 down vote accepted

This paper contains a classification of groups of order up to 30, with the exception of orders 16 and 24: Classification of Groups of Small Order by Michael Van Opstall (link, .ps file). It's not much, and I don't know anything about the paper other than what I've already written, but I think it's a good idea to have the link here in case someone stumbles on this page and doesn't come up with the idea of googling "classification of small groups".

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Thanks. Indeed, the order $16$ already is quite interesting. (M. Wild, Groups Of Order Sixteen Made Easy). – Martin Brandenburg May 13 '12 at 16:12

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