I just learned from @johncarlosbaez that are are about 50 billion groups with order less than 2000 and over 99% of them have order 1024!
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Luckily it doesn't really matter! There are lots of more interesting things to figure out. Classifying all groups of order 2048 would be like taking a census of bacteria.
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By alluding to Conway's remark, I'd hoped to hint at a broader point, which is that the classification of finite simple groups tells us about as much about finite groups as the periodic table tells us about chemistry. It's a long hike to DNA from the elements that compose it.
End of conversation
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