The purpose of this study is to describe the ability of students in constructing the concept of symmetry group. This research was conducted in STKIP PGRI Tulungagung, subjek in this research is PGSD student of Semester VI, Data collection with written test, interviews and documentation. Written tests and interviews were conducted to obtain student data in building understanding of the concept of symmetry group, While documentation is used to record all activities in building understanding of the concept of Symmetry group. The results of this study indicate that At the stage of action the subject is able to show the next steps of showing the permutation link with an equilateral triangle, At the stage of the process is able to show the next steps of imagining the reflection of the triangle, And determine reflection, At the stage of the subject object is confident with the done and able to explain the next steps of imagining the reflection properties of the triangle wake up, and determine the reflection From the nature of the reflection is changed again into a transformation composition, At the subject schema stage can already explain if the triangle is altogether converted into a rectangular or pentagonal wake, then the reflection and composition of its transformation will change, it indicates that the subject already has a scheme about symmetry group.