Hi nasty-command,
I know the differences between silk and satin, but perhaps the Asset Browser helps with the search term "Satin".
The key is certainly to have Sheen into the mix.
https://help.maxon.net/r3d/cinema/en-us/Default.htm#html/Standard_Material.html#StandardMaterial-Sheen
Use an OpenEXR HDRI in the Dome light, preferably one of the newer items of the Asset Browser. Without proper light, these kinds of fabric will not work well.
Cheers