Vol. 4, Issue 1, Part A (2022)

In this paper G be the non-abelian metabelian group and denotes the fusion class of element a in G. Fusion class is an equivalence relation. A group is metabelian group if its commutator group is abelian or if it has an abelian normal subgroup in which the factor group is also abelian. There are 35 non-Abelian metabelian groups of order less than or equal to 24. In this paper, we investigate the fusion classes of all non-abelian metabelian groups of order less than or equal to 24 and the verification has been made through GAP(Groups Algorithm Programming) software.