Humble equivalent of する. Used to describe one's own actions or in-group actions when speaking to someone of higher status. Often appears in set phrases like お願いいたします or 失礼いたします.
致し方ないthere's no other way; cannot be helped; unavoidable · it's no use (doing); pointless; useless · hopeless (person); troublesome; awful · cannot stand it; unbearable; cannot help (doing, feeling)
不徳の致すところmy fault; due to my lack of virtue; mea culpa
申し上げる
plain
N4
致す is the general humble auxiliary for 'to do', while 申し上げる as an auxiliary is reserved for attaching to お-/ご- prefixed verbs in especially formal, respect-showing contexts.