She is shown once in the books, but she does take a liking to Sophie and admires her qualities, such as her intelligence, talents, and humbleness.
“She nearly trampled a small, strange creature that looked like a cross between a sloth, a pot-bellied pig, and a small child, with fuzzy skin, an upturned nose, and a short chubby body dressed in a purple tutu.”
Empress Pernille is described to be in stage six of the troll life stages. She is short, looking like a young child, pot-bellied pig, and sloth. It was also noted that she was "chubby".