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Apr 18, 2013 at 17:40 comment added Derek Holt I am afraid that misread the definition of $H_{n,s}$ in your question. I took the definition to be $F_s/N$ where $N$ is the intersection of all normal subgroups of index exactly $n$ (rather than at most $n$, which is what you wrote). So Khalid Bou-Rabee's answer is more useful than mine for the question that you asked!
Apr 18, 2013 at 14:39 history answered Derek Holt CC BY-SA 3.0