A.T. Robertson Commentary Acts 10:48

"And he commanded them to be baptized in the name of Jesus Christ. Then prayed they him to tarry certain days." — Acts 10:48 (ASV)

Commanded (προσεταξεν). First aorist active indicative. Peter himself abstained from baptizing on this occasion (cf. Paul in 1 Corinthians 1:14). Evidently it was done by the six Jewish brethren.

Them to be baptized (αυτους βαπτισθηνα). Accusative of general reference with the first aorist passive infinitive.

In the name of Jesus Christ (εν τω ονοματ Ιησου Χριστου). The essential name in Christian baptism as in 2:38; 19:5. But these passages give the authority for the act, not the formula that was employed (Alvah Hovey in Hackett's Commentary. See also chapter on the Baptismal Formula in my The Christ of the Logia). "Golden days" (αυρε διες, Bengel) were these for the whole group.