In this paper we consider exponentiated inverted Weibull distribution. Exact expressions and some recurrence relations for single and product moments of lower generalized order statistics are derived. Further the results are deduced for moments of order statistics and lower record values and characterization of this distribution has been considered on using conditional expectation of function of lower generalized order statistics and a recurrence relation for single moments. The first four moments, mean and variance of order statistics and record values are computed for various values of parameters.