Collective nouns and subject-verb agreement: general rule or arbitrary?

A newspaper ran this headline recently:

(1) Police crack down on IAC protesters. [emph added]

Why did it not read:

(2) ? Police cracks down on IAC protesters.

I have found instances of "police cracks" in newspapers: "Police cracks whip" and "Chesterfield police cracks down on drunk drivers". However, Google's Ngram Viewer suggests that "police cracks" is significantly less frequent:

I think that the difference between "Police crack down" and "Police cracks down" is influenced by subject-verb agreement and that the difference in this example reflects the grammatical number of the verb's subject. Here, "cracks" is inflected for singular number, which implies that its subject is singular, and "crack" is inflected for plural number, which implies that its subject is plural. E.g.:

The army cracks down on IAC protesters. [singular]

The armies crack down on IAC protesters. [plural]

The confusing thing about (1) and (2) is that the subject, "police", looks like it is singular; the plural form would be "polices", but I have never heard this form (for the noun).

It sounds like police fits the definition of a collective noun, which Wikipedia says is "the name of a number (or collection) of people or things taken together and spoken of as one whole. For example, in the phrase 'a pride of lions', pride is a collective noun." Police fits this because it refers to (i) some relevant police force or (ii) some relevant group of police officers, which are both collections of people taken as wholes. It does not refer to a single police officer.

So one might conjecture that verbs whose subjects are collective nouns are inflected for plural number. However, it sounds like group also fits the definition of a collective noun because it refers to a collection of individuals taken as a whole. And I think that both of the following sound acceptable.

(3) The group crack down on IAC protesters.

(4) The group cracks down on IAC protesters.

The above conjecture also doesn't explain why it is sometimes okay to use "police cracks".

My preliminary questions: Do (1), (2), (3) and (4) all sound acceptable to everyone else? Are police and group both collective nouns?

My main questions: If (3) and (4) are both acceptable and police and group are both collective nouns, then why does (1) but not (2) sound acceptable, or at least why is "police crack" better than "police cracks"? How do you determine the correct conjugation for a verb whose subject is a collective noun? Is there a general rule, or does it vary from case to case?

My secondary questions: Does the behavior of (1) and (2) have to do with synesis? Is using police to refer to the police force more like a synecdoche or other kind of rhetorical trope? Does it matter if you add "the":

(5) The police crack down on IAC protesters.

(6) ? The police cracks down on IAC protesters.

I ask these secondary questions because I find it interesting that policeis, to me, a near synonym of police force, but police force (Ngram verb comparison) behaves oppositely to police (ngram verb comparison) when it comes to subject-verb agreement:

(7) ? The police force crack down on IAC protesters.

(8) The police force cracks down on IAC protesters.

[Note: the question mark at the beginning of an example indicates questionable grammaticality.]

Solution 1:

You're already familiar with collective nouns i.e. government, team, family. As to what verb they will take, there's a difference between British and American English:

• In American English, most collective nouns take a singular verb.
• In British English, most collective nouns can have a singular or plural verb.

But there are a few collective nouns that are always used with a plural verb in both British and American English. The most common examples are police and people.

You can read about it here.

Solution 2:

I'm unhappy about the Ngram results, especially for "police is".

In the first ten results in a Google search for "police is", I found only one relevant example.

The first few referred to enquiries of a similar nature to this one:

Police is or police are?

Several hid true subjects:

The commissioner of police is ...

The primary object of an efficient police is ...

One was of an unrelated group!:

POLICE is the Largest Street Gang in America

Even the relevant hit would seem not to constitute a reliable model:

'I will bring the truth through your (media) medium. Goa police is also narrating one sided story,' Kanda told reporters.

Intuitively, using "police crack" v "police cracks" would filter out many of these unwanted results, so I believe the first Ngram gives the truer picture. Police is usually listed in the dictionary as 'a noun of singular form (ie no -s) taking a plural construction'.

Interestingly, 'church' (not the polyseme referring to a building) is treated according to synesis in the UK:

The church are going on a picnic next week.

At this very moment, the Church is engaged in a fierce battle against the forces determined to undermine the family as God intends it to be.

Solution 3:

This one always causes problems for students, and some native speakers: "Why is it 'the army is' but 'the police are'?"

The reason is believing that police and police-force are near enough synonymous, but they are not.

The police-force is an organisation; the police are the members of the police force; and a police officer is one item of that group.

To compare this with the army, then army equates to police-force - not police. 'The police-force is' and 'the army is'.

Police equates to soldiers. 'The soldiers are' and 'the police are'.