Gwendolen has become the new "it" girl in the neighborhood. Even girls who don't like her invite her to their parties because she adds a new oomph to the social scene.
We find out that Quetcham Hall is an example of a household where Gwendolen is invited to hang out even though she's not liked there.
At her first party at Quetcham Hall, everyone's gabbing about Gwendolen. She's better-looking than the other girls there, including Miss Lawe and Miss Arrowpoint (Catherine). Mrs. Arrowpoint tells Mrs. Vulcany that Gwendolen's OK-looking until you take a good look at her.
The narrator tells us that Gwendolen has offended Mrs. Arrowpoint without meaning to. The narrator describes Mrs. Arrowpoint as "having a squat figure, a harsh, parrot-like voice, and a systematically high head-dress" (5.6).
The narrator goes on to say that it's only fitting that Mrs. Arrowpoint should have "literary tendencies" (5.6). This is sort of like saying that she has a face made for radio – she's unattractive enough that she's best at the arts where nobody sees her face.
Gwendolen gets in kind of a strained conversation with Mrs. Arrowpoint about literature. We can tell through the whole conversation that Gwendolen is trying to win Mrs. Arrowpoint over, while Mrs. Arrowpoint is looking for reasons to justify her dislike of Gwendolen.
Klesmer joins the two ladies. Mrs. Arrowpoint leaves. Klesmer and Gwendolen chat for a bit.
Then Klesmer and Catherine Arrowpoint play a duet on the piano. Catherine is really good at the piano.
Everyone wants to hear Gwendolen sing, especially Mr. Arrowpoint.
Gwendolen goes to the piano and plays and sings. Klesmer is not impressed, and he lets her know it. Gwendolen is embarrassed and avoids playing again at the party.
Then Klesmer hits up the piano for some solo action. He's really good. Gwendolen feels the music overtake her.
Clintock and Mrs. Arrowpoint ask Gwendolen to play the piano again.
Clintock asks Gwendolen if she likes the neighborhood. She says it's fine. He tells her that croquet is the game of the future, which might be one of our favorite lines of the whole novel.
Mrs. Arrowpoint decides that she doesn't like Gwendolen. Nevertheless, we find out that Gwendolen will keep getting invitations to go to Quetcham Hall because it's Catherine, and not Mrs. Arrowpoint, who is in charge of all the social invitations that go out.