Product Backlog for a system that is in production

There is no official product owner but a group of people who prioritize it.   

There you go, that's an impediment that needs to be figured out. For Scrum to be effective, there needs to be one person accountable for ordering a Product Backlog by what's most important. A Product Backlog is represented by one person, not a committee. What might be a good first step for the organization to appoint someone to fulfill the Product Owner accountability?

Our product backlog is huge and difficult to maintain.  Every component in the system is represented in the product backlog.

A Product Owner will leverage a Product Goal to help decide what's important to work on now and what isn't, and has to be respected for their decisions. The Scrum Guide reminds us that a stakeholder has to convince the Product Owner that the work is valuable and worth doing.

Large Product Backlogs are problematic because they are not transparent or easy to order. An accountable Product Owner with authority will start running the Product Backlog of everything that isn't aligned with the Product Goal, and more!

Good luck!

Does anyone in this community have any experience with this? 

Sure. That"s precisely why a Product Owner is needed in the first place, and not a committee. Establishing clear accountability for a Product Backlog, and for how value is ordered and organized upon it, comes from this experience. 

Going to join the "you need a Product Owner" bandwagon.  

This is the opening statement from the Scrum Guide's section that explains the Product Owner role.

The Product Owner is accountable for maximizing the value of the product resulting from the work of the Scrum Team. 

Remember that this is a role and not a job description.  So, the individual that does that work does not have to carry the job title of "Product Owner".  I have seen people with sales or marketing titles fulfill this role. But this statement from the Guide has to be absolutely clear to everyone in the organization.

For Product Owners to succeed, the entire organization must respect their decisions. 

In your case, your organization is violating these rules (also from the same section of the Guide)

The Product Owner is one person, not a committee. The Product Owner may represent the needs of many stakeholders in the Product Backlog. Those wanting to change the Product Backlog can do so by trying to convince the Product Owner.

As a Scrum Master, you should be evangelizing to your organization that the absence of one individual to manage the Product Backlog and maximize the work done by the Scrum Team is wasteful while also impeding the ability of the Scrum Team to be as effective as they can be. I would also suggest that your "group of people who prioritize it" makes a great start for a group of internal stakeholders that can help review and purge the Product Backlog to make it manageable under the direction of a single individual responsible for the contents of the Product Backlog (i.e. Product Owner).