Below is a character table created using the MAGMA computer algebra system.
What is the meaning of the rows starting with $p=2$, $p=3$, etc.? I've tried looking in the documentation, but couldn't find any reference to this.
I think these are the power maps described in the GAP manual here:
If I'm right line $p$, column $i$ of that section describes which conjugacy class $p$th powers of elements of class $i$ belong to. This seems to fit with the example you give.