I want to find groups whose composition factor is isomorphic to the alternating group of order 7, which groups have this condiction? best regards
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If you just want some examples, one of the examples is the symmetric group $S_7$ of degree 7. Clearly, you can costruct infinite groups that one of the its composition factors is $A_7$. For example $S_7\times\Bbb Z_p^r$ where $p$ is a prime and $r\geq 0$. 

