NSCFN-realizable group

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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

A group $G$ is termed NSCFN-realizable if it satisfies the following equivalent conditions:

$G$ can be embedded as a NSCFN-subgroup of some group.
Given any homomorphism $\alpha :L\to \operatorname {Out} (G)$ , there exists a group $K$ containing $G$ as a normal subgroup with $K/G$ isomorphic to $L$ , and the induced outer action of $G$ on $L$ is $\alpha$ .
The outer action cohomology class in $H^{3}(\operatorname {Out} (G),Z(G))$ is trivial.