  We consider Bose-Einstein condensation of noninteracting homogeneous
three-dimensional gas in canonical ensemble when both particle number $N$ and
total momentum $\mathbf{P}$ of all particles are fixed. Using the saddle point
method, we derive the large-$N$ analytical approximations for partition
function, free energy, and statistical distributions of occupation numbers of
different single-particle energy levels. At temperatures below the critical
point of phase transition, we predict, in some ranges of $\mathbf{P}$,
fragmentation of the condensate, when more than one single-particle level is
macroscopically occupied. The occupation number distributions have
approximately Gaussian shapes for the levels hosting the condensate, and
exponential shapes for other, noncondensate levels. Our analysis demonstrates
breaking of Galilean invariance of moving finite-temperature many-particle
system in the presence of Bose-Einstein condensation and extends the theory of
moving and rotating quantum systems to the finite-temperature large-$N$ limit.
