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The background of this paper is the following: search of the minimal systemsof generators for this class of group which still was not founded also problemof representation for this class of group, exploration of systems of generatorsfor Sylow 2-subgroups $Syl_2{A_{2^k}}$ and $Syl_2{A_{n}}$ of alternating group,finding structure of these subgroups.  The authors of article "Structure of 2-sylow subgroup of symmetric andalternating group" U.~Dmitruk, V.~Suschansky didn't proof minimality of findingby them system of generators for such Sylow 2-subgroups of $A_n$ and structureof it were founded only descriptively.  The aim of this paper is to research the structure of Sylow 2-subgroups andto construct a minimal generating system for such subgroups. In other words,the problem is not simply in the proof of existence of a generating set withelements for Sylow 2-subgroup of alternating group of degree $2^k$ and itsconstructive proof and proof its minimality. For the construction of minimalgenerating set we used the representation of elements of group by automorphismsof portraits for binary tree. Also, the goal of this paper is to investigatethe structure of 2-sylow subgroup of alternating group more exactly and deepthan in articlle of U.~Dmitruk and V.~Suschansky.  The main result is the proof of minimality of this generating set of theabove described subgroups and also the description of their structure. Keywords: minimal system of generators; wreath product; Sylow subgroups; group;semidirect product.

Structure, minimal generating systems and properties of Sylow 2-subgroups of alternating group