  Let $p$ be a nonzero complex number. Recently, a class of infinite rank Lie
conformal algebras $\mathfrak{B}(p)$ was introduced in [13]. In this paper, we
study the structure theory of this class of Lie conformal algebras.
Specifically, we completely determine the conformal derivations, the conformal
biderivations and certain second cohomologies of $\mathfrak{B}(p)$.
