This video explain how the symmetry groupof a square, D4, acts on a set X consists of vertices, sides and diagonals of the square. This video is based on John Fraleigh's text 16.8 Example
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Group Action On a Set Part1
Group Action On a Set Part 2
Group Action On a Set Part 3
Group Action On a Set Part 4
Group Action On a Set Part 5
Stablizer of Group Action on a set.
Fix(g) of Group Action on a set
Orbit of group action
Orbit Stabliser Theorem