What do the permissions -rwSr-xr-x mean for a binary file when it is executed as a command?

While the SetUID bit is technically present, the uppercase 'S' indicates the owner's execute permission is missing, which means the command will not be executed with the effective rights of the owner.

The 'S' is in the owner's permission field, not the group's, meaning it pertains to SetUID, not SetGID; thus, it does not relate to executing with the effective rights of the group.

The uppercase 'S' in the owner's execute position signifies that the SetUID bit is set, but the owner lacks execute permission. For the SetUID bit to be effective, the owner's execute permission (lowercase 'x') must also be set, rendering the 'S' ignored for execution with elevated privileges.

This permission set does not enable execution with the effective rights of both owner and group simultaneously, and specifically, the SetUID bit is ineffective due to the missing owner execute permission.