If you have enabled and configured DirSync you can view basic information regarding “Synchronization Status” from the Office 365 Administration Portal.
You can however, view a more detailed overview by running a simple PowerShell command.
Connect-MSOLService
Get-MSOLCompanyinformation
Using this PowerShell command you are able to determine:
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Is DirSync enabled
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What was last DirSync time of synchronization?
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What was last time of DirSync password synchronization?
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Is password synchronization enabled?