“Jack” draws upon the diaries of the real Anne Lister, who told her life story in millions of words, many of them in a code based on mathematical symbols and the Greek alphabet that was not broken until the 1890s. (Their contents weren’t published until the 1980s.) She was a woman who loved women and courted them roguishly. She was a landowner who did business with calculation. She was not a man. She simply insisted — with striking success for her time — on having the same liberties as one.

She was, above all, a presence, as the series announces by having her arrive driving a team of horses hell-for-leather into her hometown Halifax, where she has returned to take charge of her rundown ancestral home of Shibden Hall. She dismounts, brisk and commanding, looking like a steampunk-goth assassin.

Though Anne is coming home heartbroken over a lover who’s gotten engaged to a man, the scene announces that this will be no tragic story of a lesbian living furtively in a time that doesn’t understand her. Anne Lister knows the life she wants, and she has the wherewithal to decide that she will have it.

Taking over the books of the estate — over the eye-rolling irritation of her sister Marian (Gemma Whelan), perennially overshadowed by her — she sets out to exploit the estate’s coal deposits, which brings her into conflict with the foppish businessman Christopher Rawson (Vincent Franklin).

She also finds herself in want of a wife — a truth universally acknowledged for the prosperous bachelor, as Jane Austen noted. (Her preferences are an open secret in Halifax, where the gossips chirp that she “cannot be trusted in the company of other women.”)