Icosahedral symmetry - conjugacy classes and simplicity

How do we prove the rotational symmetries of icosahedron form a simple group? But wait, how do we prove any group is simple? The key to that involves the concept of conjugacy classes. This video explains intuitively why a normal subgroup has to be a union of conjugacy classes. This channel is meant to showcase interesting but underrated maths (and physics) topics and approaches, either with completely novel topics, or a well-known topic with a novel approach. If the novel approach resonates better with you, great! But the videos have never meant to be pedagogical - in fact, please please PLEASE do NOT use YouTube videos to learn a subject. This video is a continuation of the summary of my previous video series, and it is highly recommended that you watch the entire video series before this video, because there are a lot of intuitions developed throughout the video series, like conjugation is simply viewing symmetries in different perspectives. It might not make sense if you have not heard of this intuition of conjugation before. Essence of Group Theory video series:    • Essence of Group Theory   I haven't had the time to talk about centralisers and centre, which are strongly associated with the concept of conjugacy classes, because these two other concepts are less related to simplicity of the group under consideration. Maybe another video on these two concepts? Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I will probably reveal how I did it in a potential subscriber milestone, so do subscribe! Social media: Facebook:   / mathemaniacyt   Instagram:   / _mathemaniac_   Twitter:   / mathemaniacyt   For my contact email, check my About page on a PC. See you next time!