Interest in analyzing electricity consumption data of private households has grown steadily in the last years. Several authors have for instance focused on identifying groups of households with similar consumption patterns or on providing feedback to consumers in order to motivate them to reduce their energy consumption. In this paper, we propose to use electricity consumption data to classify households according to pre-defined "properties" of interest. Examples of these properties include the floor area of a household or the number of its occupants. Energy providers can leverage knowledge of such household properties to shape premium services (e.g., energy consulting) for their customers. We present a classification system - called CLASS - that takes as input electricity consumption data of a private household and provides as output the estimated values of its properties. We describe the design and implementation of CLASS and evaluate its performance. To this end, we rely on electricity consumption traces from 3,488 private households, collected at a 30-minute granularity and for a period of more than 1.5 years. Our evaluation shows that CLASS - relying on electricity consumption data only - can estimate the majority of the considered household properties with more than 70% accuracy. For some of the properties, CLASS's accuracy exceeds 80%. Furthermore, we show that for selected properties the use of a priori information can increase classification accuracy by up to 11%.