My experience is that people learn better if they have an intuitive understanding for what purpose they are learning all that stuff. This is why I would start with symmetry groups of crytsals. This ensures for instance also interdisciplinarity and something people can understand. M. Artin's book "Algebra" is really good there.

Normally, I would have advised you to tell them about the fascinating applications in differential geometry, such as the geometry of symplectic spaces. But, as you are dealing with "average undergraduates" as you named them I would use the above.

Remark: Although I would like to oppose to the nomenclature: Average undergrad at a samll college doesn't mean they shouldn't be motivated. Perhaps some of them will be fascinated by your course so intensely that they plan to go on to grad school.