The previous replies are correct. You cannot log these hours towards your flying time. It is a single pilot aeroplane and therefore (except when an instructor and student are flying together) only one person, the Pilot in Command can log the time. There's no such thing as a co-pilot in a Cessna.
Additionally because this is a syndicate operated aircraft it is almost certain that you could not claim the hours in lieu of your mate. You would not be insured to be the PIC of the aircraft. I've investigated before and you cannot nominate one person as PIC for insurance purposes and simultaneously another person for hours logging purposes.
No way round it I'm afraid. If you want to keep a record of the flights, put them in your logbook, and under Holder's Operating Capacity write Pax or Passenger and perhaps put the hours in a spare column or the margin. Do not log these hours as PIC, P1, PICUS, Pu/t, P2 or anything else.
I regularly fly with my old man in his group owned aircraft and generally 'I have control' for most of the flights. Despite being being qualified to fly the aircraft, and needing the hours, I could not find any legal way to log such time, even if he was prepared not to claim the hours himself.