terminology - What does "the ${bf N}$ of a group" mean?

In the context of group theory (in my case, applications to physics), I frequently come across the phrase "the ${\bf N}$ of a group", for example "a ${\bf 24}$ of $\mathrm{SU}(5)$" or "the ${\bf 1}$ of $\mathrm{SU}(5)$" (the integer is usually typeset in bold).

My knowledge of group theory is pretty limited. I know the basics, like what properties constitute a group, and I'm familiar with simple cases that occur in physics (e.g. rotation groups $\mathrm{SO}(2)$, $\mathrm{SO}(3)$, the Lorentz group, $\mathrm{SU}(2)$ with the Pauli matrices as a representation), but not much more. I've got a couple of related questions:

• What is meant by "${\bf N}$ of a group"?


• Is is just shorthand for an ${\bf N}$ representation? If so, what exactly is an ${\bf N}$ representation of a given group?


• How can I work out / write down such a representation concretely, like the Pauli matrices for $\mathrm{SU}(2)$? I'd be grateful for a simple example.



• What does it mean when something "transforms like the ${\bf N}$"?