The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the availability of multi-representational tools and appropriate software that can be used to bridge the existing gap between the concrete and the abstract. This paper focuses on the use of the computer program, Excel, in teaching an introductory group theory course at the university level. Here the author describes the use of the Excel 'fill-handle' and ability to colour blocks of cells as cosets quickly in constructing and completing Cayley tables for abstract groups. The relation of the approach to constructivist philosophies and cooperative learning is discussed.