You can't.
Synchronized object are only editable in your on-premises directory. Not in cloud. In that manner, setting group owner of a synchronized group does not bring any value.
The idea of group owner is to enable self-service functionalities in Azure AD. The group owner can, for example manage group memberships for the group one owns. But a synchronized group is locked for editing in cloud. Meaning that group owner will have no special privileges.
A potential solution to your task would be to configure Directory Extensions and synchronize additional group extension properties which you can later read in the cloud.