In this paper we establish the statistical properties of SGoF multitesting method under a mixture model. It is assumed that the available set of p-values is statistically independent. Special attention is paid to the huge dimension problem in which the number of tests goes to infinity. Formulae for the power and the rate of false discoveries/non-discoveries of SGoF are given, so the role of the gamma-parameter of SGoF is understood. The existing connection between SGoF and a test of significance for the proportion of non-true nulls below gamma is explored. This connection suggests a possible modification of SGoF which may improve the power of the method. Simulation studies and a real data illustration are included.
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