Was Elihu not a friend of Job?

[TonyChanYT]

Elihu seems to be a surprise character in the Book of Job. He was not introduced in the prologue. Job 2:

11 When Job's three friends, Eliphaz the Temanite, Bildad the Shuhite, and Zophar the Naamathite, heard about all the troubles that had come upon him, they set out from their homes and met together by agreement to go and sympathize with him and comfort him.

Job didn't seem to know Elihu. He never mentions him in his speeches. There was the dialogue going on with Job and his 3 friends until Job 31.

Elihu introduced himself in Job 33:

3 My words declare the uprightness of my heart, and what my lips know they speak sincerely.
4 The Spirit of God has made me, and the breath of the Almighty gives me life.
5 Answer me, if you can; set your words in order before me; take your stand.
6 Behold, I am toward God as you are; I too was pinched off from a piece of clay.
7Behold, no fear of me need terrify you; my pressure will not be heavy upon you.

He was an upright and sincere human. Elihu's speech seems like a monologue similar to God's speech afterward. God did not mention Elihu either. He was a rather mysterious character.