All possible unique combination of a single column value partitioned by groups

I have a table like the following in Google BigQuery. I am trying to get all possible unique combination(all subsets except the null subset) of the Item column partitioned on Group.

Group   Item
1       A
1       B
1       C
2       X
2       Y
2       Z

I am looking for an output like the following:

Group   Item
1        A
1        B
1        C
1        A,B
1        B,C
1        A,C
1        A,B,C
2        X
2        Y
2        Z
2        X,Y
2        Y,Z
2        X,Z
2        X,Y,Z

I have tried to use this accepted answer to incorporate Group to no avail: How to get combination of value from single column?

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