  In this work we use generalized deformed gauge groups for investigation of
symmetry of general relativity (GR). GR is formulated in generalized reference
frames, which are represented by (anholonomic in general case) affine frame
fields. The general principle of relativity is extended to the requirement of
invariance of the theory with respect to transitions between generalized
reference frames, that is, with respect to the group $GL^g$ of local linear
transformations of affine frame fields. GR is interpreted as the gauge theory
of the gauge group of translations $T^g_M$, and therefore is invariant under
the space-time diffeomorphisms. The groups $GL^g$ and $T^g_M$ are united into
group $S^g_M$, which is their semidirect product and is the complete symmetry
group of the general relativity in an affine frame (GRAF).
  The consequence of $GL^g$-invariance of GRAF is the Palatini equation, which
in the absence of torsion goes into the metricity condition, and vice versa,
that is, is fulfilled identically in the Riemannian space. The consequence of
the $T^g_M$-invariance of GRAF is representation of the Einstein equation in
the superpotential form, that is, in the form of dynamic Maxwell equations (or
Young-Mills equations). Deformation of the group $S^g_M$ leads to
renormalisation of energy-momentum of the gravitation field. At the end we show
that by limiting admissible reference frames (by $GL^g$-gauge fixing) from
GRAF, in addition to Einstein gravity, one can obtain other local equivalent
formulations of GR: general relativity in an orthonormal frame or teleparallel
equivalent of general relativity, dilaton gravity, unimodular gravity, etc.
