# Nathan Fieldsteel, Jessica Appel, Katie Davenport, Sean Grate, Madison Howard, Dave Jensen, Jenny Kenkel, Chris Manon, Owen McGrath, Jackson Morris, Laura Reese, Kate Ponto, Kathryn Schantz, and Angela Vichitbandha

The University of Kentucky Math Lab aims to encourage undergraduate
math interest across a range of projects. These include research
projects and outreach as well as visualization projects. We interpret
visualization broadly making room for both 3d printing of polyhedra,
simplicial complexes, and string diagrams and more traditional textile
crafts such as quilting and crochet.

This is a Cayley table for the symmetric group on four letters.
Each element has a color and the colors are arranged to show
subgroups and quotients. The 12 by 12 block consisting of the warm
colored squares is the alternating group on four letters. The
Klein four group is the 4 by 4 block of yellow squares. Both of
these subgroups are normal. The top 2 by 2 square is cyclic of
order 2 and not normal. To see quotients allow similar colors to
blur together. For the quotient by the alternating group blur the
warm colored squares together and the cool colored squares
together. For the quotient by the Klein four group merge the
yellow squares together and the same for orange, red, blue, green,
and purple.