Lewis & Short

paedăgōgīum, ii, n., = παιδαγωγεῖον,

  1. I. the place where boys of servile birth intended for pages were educated, the pages’ hall (not ante-Aug.), Plin. Ep. 7, 27, 13.
  2. II. Transf.
    1. A. In gen., the boys in a paedagogium: paedagogium pretiosā veste succingitur, Sen. Vit. Beat. 17, 2; id. Ep. 123, 7.
    2. B. In partic., boys reared for vice: ingenuae conditionis paedagogia, Suet. Ner. 28; cf. Plin. 33, 12, 54, § 152.