  A code is called transitive if its automorphism group (the isometry group) of
the code acts transitively on its codewords. If there is a subgroup of the
automorphism group acting regularly on the code, the code is called
propelinear. Using Magma software package we establish that among 201
equivalence classes of transitive perfect codes of length 15 from \cite{ost}
there is a unique nonpropelinear code. We solve the existence problem for
transitive nonpropelinear perfect codes for any admissible length $n$, $n\geq
15$. Moreover we prove that there are at least 5 pairwise nonequivalent such
codes for any admissible length $n$, $n\geq 255$.
