group
is a reserved key and thus can not be used as a regular identifier.
Identifier that either contain illegal characters (e.g. a space) or are reserved keywords have to be quoted with double quotes. See for example the explanation in the Postgres manual
In the SQL standard those are referred to as "delimited identifiers", but the term "quoted identifier" is also very common.
Single quotes are only used for string values in SQL (although some DBMS products allow to use double quotes for strings as well and single quotes for identifiers, that is non-standard SQL)
Note that according to the SQL standard, quoted identifiers are case-sensitive, so "Group"
and "GROUP"
are two different names (again some DBMS products ignore this as well).