cleaning af Aluminum Group chair  

a suggestion
I recently cleaned all wool upholstery on some dining chairs with just soap suds. I put a little water and a slosh of Woolite in a plastic container and shook it until the thing was full of suds.
Then using a barely-damp sponge, I worked the suds only into the fabric. Then I blotted with a big dry towel and sponged clean water onto it and blotted that.
I used a lot of the suds on some bad spots and those were hard to rinse but with a lot of blotting I finally got the suds out.
This worked really well on the light soiling. It was not quite enough for the really bad places. (These chairs looked like small children had sat on them for many, many meals.)
You can also try Goof Off, which is essentially dry-cleaning fluid, I think. But my experience with it is that it dilutes the dirt and spreads it around more. You kinda hafta do the entire piece. Plus it's a solvent and it stinks.
The good thing about wool is that it gives up dirt pretty easily.