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Going down a group has more impact on the electronegativity of an atom than going across a period. As you go down a group, there will be another valence shell added. This means that the outermost electrons feel less pull from the positive nuclear charge. Because of this, chlorine is less electronegative compared to oxygen.
A good rule of thumb when dealing with electronegativity is that as you are going across a period, generally, that has more impact than variance within a group. In other words, that electronegativity is usually closer across a period. With that in mind, even though Chlorine is in the same group as fluorine( the most electronegative atom), oxygen is in the same period, making it more electronegative.
While we generally view the trend (up and across to the right) as equally important, the truth is that going up has a bit of a greater effect on electronegativty than moving across a period. This is because the higher groups have less shells and therefore feel more pull from other atoms.
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