Language models pretrained on large collections of tabular data have demonstrated their effectiveness in several downstream tasks.However, many of these models do not take into account the row/column permutation invariances, hierarchical structure, etc. that exist in tabular data. To alleviate these limitations, we propose HyTrel, a tabular language model, that captures the permutation invariances and three more structural properties of tabular data by using hypergraphs--where the table cells make up the nodes and the cells occurring jointly together in each row, column, and the entire table are used to form three different types of hyperedges. We show thatHyTrel is maximally invariant under certain conditions for tabular data, i.e., two tables obtain the same representations via HyTreliff the two tables are identical up to permutation. Our empirical results demonstrate that HyTrel consistently outperforms other competitive baselines on four downstream tasks with minimal pretraining, illustrating the advantages of incorporating inductive biases associated with tabular data into the representations. Finally, our qualitative analyses showcase that HyTrel can assimilate the table structure to generate robust representations for the cells, rows, columns, and the entire table.