Group TS

If your Sync Rule and MPR are fine, the best approach to investigate group errors is to find the error message in connector space.
Verify the group in FIM Connector space Search by RDN and Resource ID.
In AD Connector space search by RDN and CN name.

If you are able to locate the group in FIM connector space and the state of the connector is False then the group fails to project in metavers.Find the sync errors with the group that will help to narrow down the investigation.