"Mother Grogan" is a figure in the anonymous Irish song Ned Grogan. She enters Ulysses with Mulligan's clowning about urination in Telemachus, and returns with his appearances in Scylla and Charybdis and Oxen of the Sun. What appears to have recommended her to Mulligan is her frankness about sex.
Gifford and Seidman reproduce the first verse of the song:
This commendable directness about the copulative act carries over into the joking about urination that Mulligan imagines going on between Mother Grogan and Mrs Cahill. In Oxen, he thinks also of the old woman's casual feelings about infidelity: "For answer Mr Mulligan, in a gale of laughter at his smalls, smote himself bravely below the diaphragm, exclaiming with an admirable droll mimic of Mother Grogan (the most excellent creature of her sex though 'tis pity she's a trollop): There's a belly that never bore a bastard."