  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 $\sim$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.
