  In this note we study the geometry of the largest component C_1 of critical
percolation on a finite graph G which satisfies the finite triangle condition,
defined by Borgs et al. There it is shown that this component is of size
n^{2/3}, and here we show that its diameter is n^{1/3} and that the simple
random walk takes n steps to mix on it. Our results apply to critical
percolation on several high-dimensional finite graphs such as the finite torus
Z_n^d (with d large and n tending to infinity) and the Hamming cube {0,1}^n.
