I'm developing an ETL process, and need a bridge table for a one-to-many relationship between a fact table and a dimension table (MySQL database). There is a limited number of combinations (some thousands), so I want to re-use group keys from the bridge table to to limit the size.

Any group of dimensions belonging to a fact row will consist of a number of dimension keys (1 to around 15), assigned to a unique group key, as below:

group_key | dimension_key
-----------------------
1         | 1
1         | 3
1         | 4
2         | 1
2         | 2
2         | 3
3         | 1
3         | 4

How do I go about retrieving the unique group key for the dimensions 1,3,4 (ie. 1).