in the coptic church, it's 40 days for a boy and 80 days for a girl. if you have girl and boy twins, you do them together at 80 days.
in some older traditions, the mum didn't go to church until the baby was baptized, then they would take Holy Communion together. these days, mums go to church much earlier, but don't take Holy Communion till the baby's baptism. As basically they are usually still bleeding till then.
we usually do the baptism before the morning raising of incense, then the liturgy follows and the whole family (and church) commune, then the newly baptised and family (and any other hangers-on) process around the church with the altar servers who chant and play the cymbals loudly and women ululate.
we have a quite noisy culture!