T-SQL convert rows to comma-separated string, with a GROUP BY

Hello my under-apprecitated SQL genius buddies..

I have a two-column SQL 2012 table (disguised to protect the innocent), one of which is a group name, and one is numbers

IF OBJECT_ID('tempdb..test') IS NOT NULL
   DROP TABLE #test
GO

CREATE TABLE #test (
   group_name varchar(10), 
   id int
)

insert into #test (group_name, ID) 
values 
   ('red', 101), ('red', 102), ('blue', 103), ('blue', 104), ('hazel', 105), ('mauve', 106),
   ('grape', 107), ('red', 108), ('blue', 109), ('purple', 110), ('grape', 111), ('red', 112)

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I need to generate some T-SQL, using FOR XML PATH I think but am not sure, to group by the group_name column, and return all of the ID's as a comma-separated string, like...

group_name    id_list
red              101, 102, 108, 112
blue            103, 104, 109
hazel          105
mauve        106,
grape          107, 111
purple        110

Thanks in advance.
Jim