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From the main store management page, click on Manage groups to get to the group management page. This page shows all of the groups in the store, and allows renaming or deleting them. There's also a button for adding new groups.
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The "Manage Products" page shows all of the products in your store. Select any number of products, and then select "Action > Change Groups" to change the groups that these products belong to. This action pops up a dialog that shows all of the groups in the store. The checkbox next to each group is set according to how many of the selected groups belong to that group:
Checked - if all of the products belong to the group
Unchecked - if none of the products belong to the group
"Indeterminate" - if some of the products belong to the group
The "Edit Product" Page
This page shows which groups the product currently belongs to.
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