Observations with the Chandra X-ray Observatory are used to examine the hot gas properties within a sample of 10 galaxy groups selected from the Galaxy And Mass Assembly survey's optical Friends-of-Friends group catalogue. Our groups have been screened to eliminate spurious and unrelaxed systems, and the effectiveness of this procedure is demonstrated by the detection of intergalactic hot gas in 80 per cent of our sample. However, we find that 9 of the 10 are X-ray underluminous by a mean factor of similar to 4 compared to typical X-ray-selected samples. Consistent with this, the majority of our groups have gas fractions that are lower and gas entropies somewhat higher than those seen in typical X-ray-selected samples. Two groups, which have high 2 sigma lower limits on their gas entropy, are candidates for the population of high-entropy groups predicted by some active galactic nucleus feedback models.