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We present a detailed analysis of the time decay of magnetization (M) and ac-magnetic susceptibility (χac)of hexagonal-shaped MnCo2O4 nanocrystals of average size 28 nm. The temperature (T) and magnetic field (H) dependence of the magnetization measurements reveal that even in the ferromagnetic state these nanocrystals do not exhibit conventional long-range ordering. The Curie temperature TC=176.4 K and the Hopkinson peak TH=146 K are found to be lower than those of the bulk values 184 and 175 K, respectively. Such a major decrease in TC and TH accounted for by the effect of finite-size scaling that has been thought to change the critical ordering temperatures. The dynamical properties studied by χac (T ) measurements suggest the existence of a spin-glass phase for T ≤ TF(=165 K) associated with the magnetic frustration of spins in the nanocrystals. The presence of glassy magnetic state is supported by the frequency (f) dependent studies of χac(T) and H2/3 dependence of TF in the intermediate-field region (50 Oe ≤ H ≤ 1000 Oe). Various measurement protocols including temperature quenching, step-field and wait-time dependence have been used to investigate the relaxation dynamics both in MZFC and in MFC for T ≤ TF, which show prominent memory and aging effects and supports the spin-glass state that established below TF. The magnetic viscosity (S) and microscopic spin-flip time (τ) were deduced from the time (t) dependence of MZFC using the expression M(t,T)=M(0,T)+S ln(1+t/t0) in which the magnitude of M(t) strongly depends on the wait-time spend at temperatures below TF.