what's the meaning of this sentence?
He justly thought no character so disagreeable as that of a chronic invalid , and was determined not to be one himself.

Does this sentence mean: the character can't be more disagreeable than being a chronic invalid?
what kind of the clause does " that" lead?
why there is an "of "?

Question

what's the meaning of this sentence?
He justly thought no character so disagreeable as that of a chronic invalid , and was determined not to be one himself.

Does this sentence mean: the character can't be more disagreeable than being a chronic invalid? 
what kind of the clause does " that" lead?
why there is an "of "?

Answer

This means that he does not like chronically invalid people and is determined not to be one of them.

Character here basically means personality and a disagreeable character is a personality that is undesirable. The reason 'of' is in the sentence is because the sentence is talking about the character of (belonging to) the chronically invalid.

Answer

The 'of' is there because this is a possessive form — the character of a chronic invalid. 
No character so disagreeable as that [character].

It means he found that kind of personality unpleasant.