Design a SQL-like class in Python that can perform methods on a dictionary that mimic SQL operations.
Implement a reusable query engine over one column-oriented dictionary, supporting filtering, column selection, ordering, distinct results, limits, grouping, and basic aggregations. The input table maps column names to equally sized lists, and operations are provided as a dictionary. Return an ordered list of row dictionaries with deterministic column ordering.
def execute_query(table, operations):