Translation:It is Sunday. He can not have gone to school.
Precisely. The real active verb is 'poder' and is the one conjugated. It is not so obvious in English but after 'can' and 'may' (and others: should etc) you can only put infinitives, not conjugated forms, and so happens in Spanish. Have is in infinitive and gone in past participle: puede + haber + ido.
If you want to say 'No ha ido a la escuela' then it should have been He didn't go (literally hasn't gone) to school
Berend, I understand your confusion. We expect to always see haber conjugated (he has ha hemos han) when it teams up with a gerund like IDO. But DL keeps giving us these sentences in this section on the Present Perfect in which the auxiliary verb is not conjugated. It's a curve ball for me, but I am learning it.