Unfortunately chatter group data is not copied from production to full sandbox after refresh.
So if you have to test posting to chatter group then you have to use dataloader to extract data from production and push it to sandbox.
Like usual, you have to input your credentials to production (and also check if login server is login.salesforce.com beforehand).
Then you have to select Group (CollaborationGroup) SObject and select all fields. You can also additionally specify the record id you want to copy from production to sandbox like I did in following SOQL query:
Select Id, Name, MemberCount, OwnerId, CollaborationType, Description, CreatedDate, CreatedById, LastModifiedDate, LastModifiedById, SystemModstamp, FullPhotoUrl, SmallPhotoUrl, LastFeedModifiedDate, InformationTitle, InformationBody, HasPrivateFieldsAccess, CanHaveGuests, LastViewedDate, LastReferencedDate, IsArchived, IsAutoArchiveDisabled FROM CollaborationGroup where Id = ‘0F9E00000002jA1’