The distributions are clearly positively skewed, so a normal distribution wouldn't be appropriate. Economists often seem to assume that income has a log-normal distribution, so that would probably be a good choice if it fits OK. To check that, you could log the data and then construct a normal probability plot for each group by plotting the logged percentiles (ignore the mean but include the median as the 50th percentile) against the percentiles of a standard normal distribution. If the points lie roughly on a straight line then the log-normal distribution is a reasonable fit. You could then estimate its parameters by fitting a straight line by least squares - that's not the optimal method, but it's simple and probably good enough.
Update: Just tried that myself:
Log-normal seems an reasonable fit in group 2, but not so good in group 1. I don't know if it might still be good enough for your purposes. If not you might need to go to some three-parameter distribution, but that could get a fair bit more complicated.