COMPUTING THE PRODUCTS OF CONJUGACY CLASSES FOR SPECIFIC FINITE GROUPS

Suppose $g$ is a finite group, $a$ and $b$ are conjugacy classes of $g$ and $eta(ab)$ denotes the number of conjugacy classes contained in $ab$. the set of all $eta(ab)$ such that $a, b$ run over conjugacy classes of $g$ is denoted by $eta(g)$.the aim of this paper is to compute $eta(g)$, $g in { d_{2n}, t_{4n}, u_{6n}, v_{8n}, sd_{8n}}$ or $g$ is a decomposable group of order $2pq$, a group of order $4p$ or $p^3$, where $p$ and $q$ are primes.