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Let   $\mathscr{B}_0({\mathcal{G}})\subseteq k\,{\mathcal{G}}$   be the principal block algebra of the group algebra   $k\,{\mathcal{G}}$   of an infinitesimal group scheme   ${\mathcal{G}}$   over an algebraically closed field   $k$   of characteristic   ${\operatorname{char}}(k)=:p\geq 3$  . We calculate the restricted Lie algebra structure of the first Hochschild cohomology   ${\mathcal{L}}:={\operatorname{H}}^1(\mathscr{B}_0({\mathcal{G}}),\mathscr{B}_0({\mathcal{G}}))$   whenever   $\mathscr{B}_0({\mathcal{G}})$   has finite representation type. As a consequence, we prove that the complexity of the trivial   ${\mathcal{G}}$  -module   $k$   coincides with the maximal toral rank of   ${\mathcal{L}}$  .

On the First Hochschild Cohomology of Cocommutative Hopf Algebras of Finite Representation Type