Munywoki, MichaelKamuti, IreriKivunge, Benard2015-05-292015-05-292010International Electronic Journal of Pure and Applied Mathematics Volume 1 No. 3 2010, 339-344http://e.ijpam.eu/contents/articles/201000103010.pdfhttp://hdl.handle.net/123456789/1178There are several very useful formulas, which give the cycle indices of the binary operation of the sum, product, composition and po wer group of M and H in terms of cycle indices of M and H . One very useful binary operation on groups, which has not been exploited, is the semidirect product. Suppose G = M ⋊ H , a semi direct product; the question is: how can we express the cycle index of G in terms of the cycle indices of M and H ? This work partially answers this question by considering the cycle indices of so me particularly semidirect product groups; namely – Frobenious groupsenArticle