Abstract: In this talk, we will prove that the group of symmetries of a standard (3x3x3) Rubik's cube is isomorphic to (\mathbb{Z}_37 \times \mathbb{Z}_2^{11}) \rtimes ((A_8 \times A_{12}) \rtimes Z_2). Due to limited time, some proofs may not be completely rigorous. We will also try to understand how the above structure suggests a natural commutator based approach to solving the Rubik's cube (and also how it generalizes to higher order cubes).
The talk will assume a very basic group theory background, namely knowledge of cyclic groups and direct products. We will define semidirect products and alternating groups through the course of the talk.
