We consider the family of irreducible cyclically presented groups on n generators whose generating word (in the standard rewrite) has length at most 15. Using the software packages KBMAG, quotpic and Magma, together with group and number theoretic methods, we show that if 6 ≤ n ≤ 100 then the group is non-trivial. In an appendix we list the 47 cases within 2 ≤ n ≤ 100 for which we know the grou...
