The paper analyzes the infrastructure of public schools in Brazil by examining the hypothesis that the institutions with poor material conditions have students with a lower socioeconomic level. The characterization of the institutions is based on data from the 2013 School Census, submitted to latent class modeling, which revealed the existence of four different school profiles. In order to carry out a socioeconomic differentiation of the institutions, the Poverty In School Indicator (IPE in Portuguese) was created, which uses data from Bolsa Família, an income transfer program. The results confirm the available body of literature on the subject by showing that the location, the administrative dependency, the size of the school and the region of the country in which it is inserted are related to the inequalities of school infrastructure. In addition, the study finds that the public schools with better infrastructure conditions generally have lower proportions of poor students. On the other hand, most institutions with the worst infrastructure profile have mostly poor or extremely poor students, confirming the hypothesis of this research.

We analyzed the infrastructure conditions of Brazilian schools, aiming to expose their inequalities and territorial distribution. The literature review pointed an influence on previous studies of school infrastructure of regulation by outcomes on the educational system coordination and the limits of current redistributive policies in promoting greater inter federative equity. We tested the hypothesis of a poor school for the poor using the clusters analysis (use of K-means after application of hierarchical method, to determine the number of clusters and centroids). The three clusters obtained (adequate, intermediate and precarious) allowed us to trace the profiles of school infrastructure inequalities by constructing reference variables that expressed the quality of the good or service. Among the results obtained, there was a greater number of students from families participating in the “Bolsa Família” Program in public schools located in urban areas in the group called “adequate”, according to Brazilian standards. There was also a higher concentration of these students in municipal schools in rural areas of the “precarious” group, despite the reduced number of enrollments by Brazilian standards. We concluded by relating the reasons for the invisibility of these schools to the agendas of national public education policies.