We need to merge the group in order to nudge the selection.
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Select the group from Layers palette (pressing Ctrl+E is going to do the job of two lines below)
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Right-click on the group
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Choose Merge Group
Hint: It's better to duplicate the group and hide it before merging so that we can edit layers in the group when we need them.
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Select the group from Layers palette
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Right-click on the group
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Choose Duplicate Group...
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To hide this group, click the "eye" icon next to its thumbnail