The 2002 movie musical "Chicago" features a black woman as a prison warden. Would this position of power have been available to a woman of color in 1920s Chicago?

While giving this lovely movie a watch, the question struck me - how plausible is the character of "Mama"? She's a black woman serving as the Warden of a women's prison in 1920s Chicago. Given the reduced opportunities for both women and people of color at that point in history, I got curious. Wasn't sure how to look into that myself!