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Nov 20, 2023 at 10:50 comment added Sean Eberhard I agree with @YCor that my answer should not be accepted in its current form. Although I think it almost certain that such a group $S$ does not exist, it's not obvious, and I would be interested to see the demonstration. Also, I am actually not at all sure that $G = \prod_F F$ has no countable quotient covering every finite group, it was just a thought.
Nov 16, 2023 at 10:13 vote accept Dominic van der Zypen
Nov 20, 2023 at 12:47
Nov 15, 2023 at 19:59 vote accept Dominic van der Zypen
Nov 15, 2023 at 20:07
Nov 15, 2023 at 16:54 history undeleted Sean Eberhard
Nov 15, 2023 at 16:54 history edited Sean Eberhard CC BY-SA 4.0
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Nov 15, 2023 at 10:42 history deleted Sean Eberhard via Vote
Nov 15, 2023 at 10:38 history answered Sean Eberhard CC BY-SA 4.0