The following is a visualization of the matrices which show up in a certain 3 dimensional representation of the simple group of order 168. The white concentric circles denote the three roots of x^3+x^2-1/7, and the full white circle denotes 1. The six colored versions of these indicate multiplying by a seventh root of unity. For example, the top left is the identity matrix, and the top row is a subgroup of order 21. Note also that the leftmost columns is a Sylow 2-subgroup.