Group is the Metadata type for retrieving and deploying Public Groups in Salesforce. It also includes Queues. So, check the export before deploying them into another org.

The following Package.xml will pull all the Public Groups and Queues configured in the Salesforce Org.

Sample Package.xml:

<?xml version="1.0" encoding="UTF-8"?>  
<Package xmlns="">  
  
    <types>  
        <members>*</members>  
        <name>Group</name>  
    </types>  
  
    <version>31.0</version>  
  
</Package>