A word to describe someone who is oblivious to the atmosphere in a group conversation
Solution 1:
I would use not tactful for such a person as tactful means:
careful not to offend or upset other people: having or showing tact (a keen sense of what to do or say in order to maintain good relations with others or avoid offense)
"(S)he behaves tactlessly." could also work. Tactless is usually used attributively modifying a noun:
tending to offend or upset people: not showing or having tact: 'tactless comments'
[Merriam-Webster]
Solution 2:
A word to describe someone who is oblivious to the atmosphere in a group conversation would be incognizant.
incognizant (ĭn-kŏg′nĭ-zənt)
lacking knowledge or awareness. –Google
lacking awareness or consciousness. incognizant of the danger –MW
lacking knowledge or awareness; unaware: incognizant of the new political situation. –TFD
incognizant (often followed by `of') not aware; "seemed unaware of the scrutiny"; "unaware of the danger they were in"; "unaware of the newborn hope"; "the most unaware person I've known" –TFD
"I felt as comfortable as I have ever felt when speaking in public, wholly incognizant of my trapezius muscle or bodily fluids." –vocabulary.com
Urban Dictionary : #incognizant
"Oblivishit"
Lacking remembrance, memory, or mindful attention, but wouldn't give a shit anyway.
synonyms of Oblivious, thesaurus.com :
See, clueless. Also; is not to be confused with this author's attitude of: "IDGAF".
Solution 3:
I think "gauche" above covers things pretty well. It comes from the French for "left", so it implies someone who just does things a little wrong.
English also has a term "reading the room". It means being observant to see if your behavior fits in with the how other people are behaving, usually in the sense of whether or not your topic of conversation is considered acceptable. But it's not used as a general descriptor for a person, just as a descriptor for what a person is, or more frequently, is not doing at that moment.
"Psst. Read the room. No one hear wants to hear you talk about how great your divorce lawyer is at a wedding."
Solution 4:
As to the person who blathers on and on, oblivious to the needs, interests, and desires of the other people in a discussion, I'd call that person a conversation hog.
An indelicate way of confronting such a person might be
Hey! Quite hogging the conversation!
A more delicate way, as a teacher of elementary school children might say to a pupil who is hogging the conversation,
Now Johnny, let's give someone else a turn to talk.
At the heart of hogging a conversation is a kind of egotism coupled with a lack of empathy. A good conversationalist reads any number of things in a group discussion, including people's affects, gestures, level of interest in what's going on, and so much more. There is a certain dance of etiquette which proceeds smoothly when participants are adept at reading the situation, or milieu, and behave accordingly.
I remember talking one-on-one to a fairly famous person during an after-speech reception. His speech had included a question and answer period at the conclusion of his prepared remarks, so I confidently approached the gentleman during the reception with an apropos follow-up question, which he answered graciously and intelligently.
Somewhat unbeknownst to me, a small group of people had gathered nearby the speaker and me. Quite deftly and subtly he gestured and moved his body in such a way that the small group felt they were being invited into the ongoing discussion.
Now I wouldn't characterize my one-on-one discussion with the speaker as "hogging the conversation," but the gentleman, sensitive enough to realize other folks were waiting to talk with him, made a conscious effort to widen the circle, so to speak. I never forgot that.
As good as one-to-one conversations can be when they take place privately, apart from other folks, when they take place where other people are milling about, eager to engage others in conversation, "the more the merrier," I say. That is particularly true when a respected expert or authority has just given a speech and the after-party is filled with people who may not have the confidence to approach the speaker one-on-one. Those same people may perhaps feel free to join a group-discussion if they sense the speaker is amenable to it. Again, the more the merrier.
The conversation hog, on the other hand, would resent such an "intrusion"!