On Simple and Regular Permutation Groups of Degree 3p - Numerical Approach

Let G be a dihedral group of degree 3p that are not p-groups. Several survey articles in the research space written about the implications of the classification of finite simple group for permutation groups and related areas. Determination of the properties of permutation groups as simple, regular, nilpotency, transitivity, primitivity and solvability of various categories of groups have been carried out with a view to classify finite permutation groups of certain degree is still of interest to many mathematicians. Our result showed that all Groups of degree 3p that are not p-groups are not simple and irregular. We used some theorems and a computer programme – Groups, Algorithms and Programming (GAP) to enhance and validate our findings.