The maximum phase of the solar cycle is characterized by several interesting features in the solar activity, heliospheric characteristics and the galactic cosmic ray (GCR) intensity. Recently the maximum phase of the current solar cycle (SC) 24, in many relations anomalous when compared with solar cycles of the second half of the 20-th century, came to the end. The corresponding phase in the GCR intensity cycle is also in progress. In this paper we study different aspects of the sunspot, heliospheric and GCR behavior around this phase. First, the amplitudes of the SC 24 in the solar activity and GCR intensity are considered and compared with the previous sunspot cycles. Second, the inversion of the heliospheric magnetic field is studied for SC 21-24 using the suggested classification of its polarity distributions. Third, the GCR-effects specific for the maximum phase of SC 21-24 are considered and correlated with the behavior of the heliospheric magnetic field's strength and with the inversion of its polarity. Our main conclusions are as follows:1. The maximum phase of the sunspot SC 24 ended in 06.2014, the development of the sunspot cycle being similar to those of SC 14, 15 (the Glaisberg minimum). The maximum phase of SC 24 in the GCR intensity is still in progress.2. The inversion of the heliospheric magnetic field consists of three stages, characterized by the appearance of the global heliospheric current sheet (HCS), connecting all longitudes. In two "transition dipole" stages beside the global HCS there are additional local HCSs, while the "inversion" stage lies between two "transition dipole" ones and there is no global HCS in this stage. The "inversion" stage of the current SC 24 is the longest when compared with those for SC 21-23. The second "transition dipole" stage and hence the whole inversion period of the heliospheric magnetic field in SC 24 provisionally ended in 08.2014.3. The behavior of the GCR intensity in the period of the sunspot maximum phase and the inversion of the heliospheric magnetic fields for SC 21-23 demonstrates all the characteristic features for this period: the two-gap structure corresponding to two-peak structure in the sunspot activity, and the energy hysteresis. In the current SC 24 the GCR intensity shows rather unusual features and we should wait for one or even two years to see the whole picture.