SELECT 
  f.feature_id, 
  f.purpose, 
  p.product_id, 
  p.parent_product_id, 
  g.id, 
  g.code 
FROM 
  cscart_product_variation_group_features AS f 
  INNER JOIN cscart_product_variation_groups AS g ON f.group_id = g.id 
  INNER JOIN cscart_product_variation_group_products AS p ON f.group_id = p.group_id 
WHERE 
  p.product_id IN (827, 1578, 831, 833, 1576, 832)

Query time 0.00085

JSON explain

{
  "query_block": {
    "select_id": 1,
    "nested_loop": [
      {
        "table": {
          "table_name": "p",
          "access_type": "range",
          "possible_keys": ["PRIMARY", "idx_group_id"],
          "key": "PRIMARY",
          "key_length": "3",
          "used_key_parts": ["product_id"],
          "rows": 6,
          "filtered": 100,
          "index_condition": "p.product_id in (827,1578,831,833,1576,832)"
        }
      },
      {
        "table": {
          "table_name": "f",
          "access_type": "ref",
          "possible_keys": ["idx_group_id"],
          "key": "idx_group_id",
          "key_length": "3",
          "used_key_parts": ["group_id"],
          "ref": ["dev_db.p.group_id"],
          "rows": 1,
          "filtered": 100
        }
      },
      {
        "table": {
          "table_name": "g",
          "access_type": "eq_ref",
          "possible_keys": ["PRIMARY"],
          "key": "PRIMARY",
          "key_length": "3",
          "used_key_parts": ["id"],
          "ref": ["dev_db.p.group_id"],
          "rows": 1,
          "filtered": 100
        }
      }
    ]
  }
}