We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that the most efficient design for simultaneously estimating the prevalence, sensitivity, and specificity requires three different group sizes with equal frequencies. However, if estimating prevalence as accurately as possible is the only focus, the optimal strategy is to have three group sizes with unequal frequencies. Based on a Chlamydia study in the United States, we compare performances of competing designs and provide insights into how the unknown sensitivity and specificity of the test affect the performance of the prevalence estimator. We demonstrate that the proposed locally D- and Ds-optimal designs have high efficiencies even when the prespecified values of the parameters are moderately misspecified. Extensions on budget-constrained optimal group testing designs will also be discussed, where both subjects and tests incur costs, and assays have uncertain sensitivity and specificity that may be linked to the group sizes.