。
She isn't home — she's at school.
Literal
She [topic-は] home [at-に] not-be [and-て], school [to-に] is-going.
The negative te-form ~なくて links two clauses with a state-of-affairs reason or contrast: 'not X, and (instead/so) Y.' Compared to ~ないで (which means 'without V-ing'), ~なくて leans more toward stating a state. Here the structure is 'she's not at home, and (so) she's at school.' The verb 行っている here is ~ている as a resulting state — she has gone there and is currently in that state, rather than 'is in the act of going.' Useful contrast: the same form can signal ongoing or resulting state depending on the verb's lexical aspect.