Given a finite group $G$ with irreducible character $\chi \in \Irr(G), \hspace{1ex} r \in {\mathbb N}$ and a partition $\lambda$ % \vdash of $r$, we define higher characters $\chi_{\lambda}^{(r)}$ of $G$, following Frobenius \cite{Frob}. We interpret them as a generalization of Schur functions in noncommuting variables, as a multilinear invariant map, as the sum over $\S_r$ of a character of the wreath product $G \wr \S_r$, and as the trace of a $e_\lambda G_r e_\lambda$-module. Using these interpretations, we are able to compute $(\chi + \psi)_\lambda^{(r)}$ in terms of $\chi_\mu^{(a)}$ and $\psi_\nu^{(b)}$ where $a+b=r$ and $\mu$ and $\nu$ are partitions of $a$ and $b$, respectively. We show distinct higher characters are orthogonal in section \ref{orthog_sec}. These $\chi_{\lambda}^{(r)}$ have the property that they are constanton $\S_r \times G$ orbits of $G^r$, %% i.e. invariant under diagonal conjugation and permutation of entries of an r-tuple. By decomposing ${\Hom}_{G_r}({\Ind}_{\S_r}^{G_r} E_{\lambda}, {\Ind}_{\S_r}^{G_r} E_{\lambda}) = e_\lambda G_r e_\lambda$, we find an orthogonal family of functions with this property. In the case $G$ is abelian, we show this family forms a basis for all such functions on $G^r$. This doesn't happen for general $G$, as shown on some examples in the appendix. However, in both cases, we show that it is only necessary to consider $\lambda = (r)$ (or $\lambda = (1^r)$) in theorems \ref{bas} and \ref{abbas}. % The reader may skip straight to section \ref{subsec_w} for these results.