You should take the below steps to construct a strategic group map for an industry:

1. Identify key competitors: The first step is to identify the key competitors in the industry. These competitors should be those that are most relevant to the company being analyzed.

2. Identify relevant factors: The next step is to identify the key factors that are most important in the industry. These factors can include price, quality, technology, distribution channels, and customer service, among others.

3. Plot the factors: Once the key factors have been identified, they should be plotted on a graph. The x-axis should represent one factor, and the y-axis should represent another. This will create a two-dimensional map.

4. Identify strategic groups: The next step is to identify the strategic groups within the industry. This can be done by analyzing the data on the graph and grouping companies that are similar in terms of their performance on the two key factors.

5. Determine the characteristics of each group: Once the strategic groups have been identified, it is important to determine the characteristics of each group. This can include factors such as market share, growth rate, profitability, and other relevant metrics.

6. Analyze the map: Finally, the map should be analyzed to determine what insights can be gained from it. This can include identifying areas where the company is positioned relative to its competitors, as well as identifying potential opportunities and threats within the industry.