Does Google have a record of my fingerprints from the Android devices?
No, your fingerprint data never leaves your device.


  Your fingerprint data is stored securely and never leaves your Pixel or Nexus phone. Your fingerprint data isn't shared with Google or any apps on your device. Apps are notified only whether your fingerprint was verified.


Source

Source is from Nexus/Pixel support pages hence why it mentions them specifically. The same should apply for other devices however)