Thanks everyone for making this a great semester. I had a lot of fun teaching this class!

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Visualizing the generators of Z_7:

Visualizing Z_12 and its subgroups:

Group table for S_4, ordered by cosets of subgroup
generated by rho_1 (subgroup of rotations in D4):

Group table for S_4, ordered by cosets of a subgroup that is isomorphic
to V_4: