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How do I get the list of customers who ordered a product of a specific brand?

With Segmentation tool, you can get in Store Commander the list of all customers who ordered at least one product of a specific brand.

Create an automatic segment displayed in the Customer interface using the type 'Customers who ordered product of manufacturer' and select the name of the brand in the drop down menu:

Now you just need to select that segment in the Customer interface and the list of corresponding customers will be displayed.