The point of view of Muriel Spark's novel, The Pride of Miss Jean Brodie, is third person omniscient. A third person omniscient narrator, who provides point of view, is able to relay the actions, thoughts, feelings and motives of any character, at any time throughout the novel.
In the Pride of Miss Jean Brodie, sometimes the third person omniscient point of view operates through Miss Brodie, for example when she requests a cartwheel be done for "comic relief." At other times it operates through one or other of the girls as when Sandy is with Sargent Anne talking about acquiring evidence against Miss Brodie. Or it may operate through a lesser character as when Miss Mackay interviews Sandy regarding exposing Miss Brodie.
Yes, third person omniscient yet the narrator is an intrusive narrator who has a tendency to mock Brodie and her actions and attitudes. The entire narrative structure is very important because Spark informs us all, early in the novel, what the outcomes are going to be for many characters (Brodie's betrayal, Sandy's becoming a nun, Mary's death in a fire) and this makes the reader focus on how the outcomes are arrived at. The narrative then drip-feeds the information through these narrative shifts in point of view. Very clever and deceptively powerful.