The transfer function of a system is a mathematical function that relates the output of the system to its input. It can be used to calculate the output of the system for any given input, as well as the steady state gain of the system. The order of the system and the time constant are not directly related to the transfer function.
The transfer function of a system is typically written in the form
$H(s) = \frac{Y(s)}{X(s)}$
where $Y(s)$ is the output of the system, $X(s)$ is the input to the system, and $s$ is the Laplace transform variable. The transfer function can be used to calculate the output of the system for any given input by taking the Laplace transform of the input and multiplying it by the transfer function.
The transfer function can also be used to calculate the steady state gain of the system. The steady state gain is the value that the output of the system approaches as time goes to infinity. It can be calculated by taking the limit of the transfer function as $s$ approaches infinity.
The order of the system is the number of poles in the transfer function. The time constant is the time it takes for the output of the system to reach 63.2% of its steady state value. The order of the system and the time constant are not directly related to the transfer function.