The order of who washes first:[1]

If a group of people ate together and are now reciting Birchas Hamazon, then if there are more than five people present, the youngest of the group who is sitting at the end is to be the first to wash Mayim Achronim.[2] The water is then given from there and onward, without honoring anyone first, until they reach the last five people.[3] Once the last five people in the group are reached, the leader who will be saying Birchas Hamazon is to be the first to wash, and the rest are then given to wash without any order. Likewise, if to begin with there are only five or less people present, then the leader of the Zimun is to be the first to wash Mayim Achronim.[4] [Practically, today the custom is to place a few cups of Mayim Achronim on the table and everyone does it together.[5] Furthermore, the widespread custom today is to honor the person who will lead Birchas Hamazon with the performance of Mayim Achronim even if there are more than five people present.[6]]

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[1] Admur 181:6; Michaber 181:6; Ketzos Hashulchan 43:1

[2] The reason: We do not honor the eldest or leader with washing as in fact it is a disgrace for him to be the first to wash and then wait for everyone else to wash. Therefore, we begin with the youngest who is sitting at the end, and the leader and elder can continue eating or doing something else until the water reaches him. [Admur ibid]

[3] The reason: It is unbefitting to honor others with toxic hands. [Admur ibid]

[4] The reason: Within the last five, or a group of five, the person who will lead the Bentching is to be given to wash first in order so he can prepare the reading in the interim. The amount of time it takes for four more people to wash, was estimated by the Sages to be enough time to prepare all four blessings, as well as to not be considered an interval between the washing and blessing. [Admur ibid]

[5] Biur Halacha 181:6 “Min Hakatan”

[6] Kitzur SHU”A 44:1; See Piskeiy Teshuvos 181:10