The default Symphony Desktop Application (SDA) installation path will differ depending on the installation type that is selected.
When installing for all users, the default installation path will be C:\Program Files\Symphony\Symphony (Figure 1 and Figure 2):
Figure 1 Installation For All Users 1
Figure 2 Installation For All Users 2
When installing for a single user, the default installation path will be C:\Users\[UserName]\AppData\Local\Programs\Symphony\Symphony (Figure 3 and Figure 4):
Figure 3 Installation For A Single User 1
Figure 4 Installation For A Single User 2
Note: The installation path can be manually amended at a later date if needed (Figure 5):
Figure 5 Installation Path
Refer to the Knowledge Article found here on silent installs of the SDA.