How to get the group info (name or id) before the ticket is assigned to another group?

What attribute are you using to look at the results from this metric? For example, if you were using Updates, this formula would return the count of Update IDs for any ticket update, where the group changed from not set, to set, and would return the group_id that the ticket was assigned to on that update. 

You mention specifically you are trying to get the group that a ticket was assigned to, before it was assigned to another group. Let's call the groups "Tier 1" with a pretend group_id of 01 and "Tier 2" with a pretend group_id of 02. If you wanted to know every ticket where a ticket was passed from tier 1 to Tier 2, you would want to do: 
If [Changes - Field name]= "group_id" and [Changes - Previous value] = "01"
and [Changes - New value] = "02"
THEN
[Ticket ID]
endif

This would return a ticket ID for every ticket where there was an update to the ticket at some point, that changed the group from Tier 1, to Tier 2.  Is that the kind of thing you were looking for? 

Actually, my question is like below

One ticket is changed to different groups automatically, I need to locate the group name which is marked with blue edge rectangle.

The difficulty is there are many groups can be assigned to by Zendesk automatically, I cannot only rely on the formula to write down all group id.