I have to answer 2 questions on the alternating group $A_{4}$:
One of them asks me to find all irreducible complex representations of the group $A_{4}$ (and calculate their characters) while the other one asks me to find all 1-dimensional representations of $A_{4}$. I have answered the second question without using the character table. but I feel like the answer of the first question like the second one, could anyone explain the difference for me please?
Thank you!