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A Pfaffian-type Murnaghan-Nakayama rule is derived for the Hecke-Cliffordalgebra $\mathcal{H}^c_n$ based on the Frobenius formula and vertex operators,and this leads to a combinatorial version via the tableaux realization ofSchur's $Q$-functions. As a consequence, a general formula for the irreduciblecharacters $\zeta^{\la}_{\mu}(q)$ using partition-valued functions is derived.Meanwhile, an iterative formula on the indexing partition $\la$ via the Pierirule is also deduced. As applications, some compact formulae of the irreduciblecharacters are given for special partitions and a symmetric property of theirreducible character is found. We also introduce the spin bitrace as theanalogue of the bitrace for the Hecke algebra and derive its generalcombinatorial formula. Tables of irreducible characters are listed for$n\leq7.$

Murnaghan-Nakayama rule and spin bitrace for the Hecke-Clifford Algebra