Hello,
Basically, the term Group Manager refers to the Technical/Operations team, whereas General Manager refers to the Support/Management Teams. Hence, both can't be compared in a manner that determines who is higher in the hierarchy. Again, it differs from organization to organization and from industry to industry.
A Group Manager can be related to a Senior Manager/Head of Department for a specific team. A General Manager can be related to the company as a whole or specifically to a department.
Regards,
Chandana Hyma