This is possible with a scripting automation. With the base structure shown in your screen shots, it is not possible without code.
However, I suggest that you investigate a different base design. Your table structure looks like you are familiar with spreadsheets. Despite the visual similarity to a spreadsheet, Airtable is not a spreadsheet–it is a database. Here is some food for thought:
- Take advantage of linked record fields to join the two tables, instead of copying the name to the text field in the [Groups] table.
- If the position of the members (who is 1st, 2nd, 3rd, etc) does not matter, you can use one linked record field in the [Groups] table for all of the members. You can use count or rollup fields to determine the total number of members.
- If the position of a member is important, can someone belong to multiple groups? If a person can belong to only one group, you can store the position in a numeric field or automatically calculate a position.
- If you want to increase the number of members in a group, you will need to change your current base design. However, there are other more flexible base designs that can handle changes in the number of members per group without changing your base design.
By the way, based on your screen captures, it looks like you have a one-to-many relationship, not a many-to-many relationship. One group can have many members, but each member belongs to only one group.