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What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$?

 

Is there a compact manifold which can be act freely by all symmetric groups $S_{m}$?

This question have been asked already here and is indirectly related to this.

What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$?

Is there a compact manifold which can be act freely by all symmetric groups $S_{m}$?

This question have been asked already here and is indirectly related to this.

What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$?

Is there a compact manifold which can be act freely by all symmetric groups $S_{m}$?

This question have been asked already here and is indirectly related to this.

What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$?

Is there a compact manifold which can be act freely by all symmetric groups $S_{m}$?

This question have been asked already here and is indirectly related to this.

What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$?

Is there a compact manifold which can be act freely by all symmetric groups $S_{m}$?

This question have been asked already here and is indirectly related to this.

What type of compact manifolds, can be acted freely by symmetric group $S_{m}$ for some $m>2$?

Is there a compact manifold which can be act freely by all symmetric groups $S_{m}$?

This question have been asked already here and is indirectly related to this.