Imagine

Imagine
 

p.326
-Harry imagined coming here with Dumbledore, of what a bond that would have been, [...]

Does it prove we could say we 'imagine of sth'?

Here, 'of' is a preposition, and the 'something' that is imagined is found in the prepositional phrase. This is allowed, but there are many other times when a prepositional phrase is not playing the role of the direct object.

What do you imagine of the future?
(What do you imagine about the future?)
What do you imagine the future to be like?

You may imagine of what importance there is in working.
You may imagine what importance there is in working.

In American English, we don't use a prepositional phrase to complete the verb 'imagine' as often as the British do.
By the way, the British also use 'imagine of' to mean 'picture of'.

Thank you, but what does 'picture of' mean? I've never seen it in a dictionary.

???eg I pictured of what he would look like in clothes like that and laughed.

I should have added an article for clarity, and probably shouldn't have confused the issue with an unrelated grammatical example. Sorry about that.

This is an imagine of us at the zoo. (British English)
This is a picture of us at the zoo. (American English)


By the way,
"I pictured what he would look like in clothes like that and laughed." = "I imagined what he would look like in clothes like that and laughed."
Note that neither of these synonymous examples has a prepositional phrase playing the role of the direct object; there is a noun clause in that role, introduced with the relative conjunction 'what'.
In fact, the quotation from the book in the initial post, where 'imagined' is followed by 'coming', is another example of a direct object immediately following the verb; 'coming' is a gerund (which is always a noun) and it is the verb's object.
Indeed, the writer could have omitted the introductory preposition in the second clause, starting it with the relative conjunction 'what', and it would still make perfect sense.
-Harry imagined coming here with Dumbledore, what a bond ...

Um...but you still think 'John imagines of something' is correct but less common?

The last sentence you wrote would not be heard in American English.

Thank you~