Calculate the character degrees of a finite group $G$.

Let $$G$$ be a finite group and $$K$$ be a group of order $$8$$. Suppose that $$G/K\cong M_{12}$$ where $$M_{12}$$ is one of the Mathieu group.

QUESTION:

How to calculate the all complex character degrees of $$G$$?

• What can you deduce about the extension of $K$ by $M_{12}$? Can it be non-split? – ahulpke Feb 11 at 23:30