  In this work the algorithms of fast multiplication of matrices are
considered. To any algorithm there associated a certain group of automorphisms.
These automorphism groups are found for some well-known algorithms, including
algorithms of Hopcroft, Laderman, and Pan. The automorphism group is isomorphic
to $S_3\times Z_2$ and $S_4$ for Hopcroft anf Laderman algorithms,
respectively. The studying of symmetry of algorithms may be a fruitful idea for
finding fast algorithms, by an analogy with well-known optimization problems
for codes, lattices, and graphs.
  {\em Keywords}: Strassen algorithm, symmetry, fast matrix multiplication.

Computational Complexity;Data Structures and Algorithms;Group Theory