There exist $49910529484$ finite groups of order at most $2000$. Among these, $49487365422$ (that is, more than $99 \%$) have order $1024$.
References.
[1] https://www.math.auckland.ac.nz/~obrien/research/2000-announce.pdf
[2] https://math.stackexchange.com/questions/241369/more-than-99-of-groups-of-order-less-than-2000-are-of-order-1024
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