Date of Award


Document Type


Degree Name

Master of Arts in Mathematics



First Reader/Committee Chair

Dr. Zahid Hasan


In this thesis we have discovered homomorphic images of several progenitors such as 3^(*56):(23:(3:7), 3^(*14):(23:(3:7)), 5^(∗24) : S5, 2^(∗10) : (10 : 2), 56^(∗24) : (A5 : 2), and 11^(∗12) :m L2(11). We give isomorphism types of each image that we have found.
We then create a monomial representation of L2(11) by lifting 5:11 onto it.
We manually perform Double Coset Enumeration of 3:(2×S5) over D12
to create its Cayley graph. This is achieved by solving many word problems. The
Cayley graph is used to find a permutation representation of 3:(2×S5). We also
perform Double Coset Enumeration S3 × A5 over 15:2 and 10:2, where 15:2 is a
maximal subgroup containing 10:2.
Finally, a code based algorithm is included that solves all of the word
problems used to perform Double Coset Enumeration of L2(25) over S5:2 and
Double Coset Enumeration of (A5)2:2 over A5:2