Let $V$ be an $n$-dimensional real vector space, $\Lambda\subseteq V$ a lattice, and $K$ a subgroup of $Aut_{\mathbb{Z}}(\Lambda)\cong GL(n,\mathbb{Z})$. Let also $\sigma \in Z^1(K,V/\Lambda)$, $\sigma:K\to V/\Lambda$, be a cocycle, and $s:K\to V$ a lift of $\sigma$. Define

$K \ltimes^{\sigma} \Lambda:=\{ (k,\lambda + s(k))\in K\times V\; | \; k\in K,\; \lambda \in \Lambda \}\subseteq K \times V.$

Does the above construction have a name (maybe in more general form)? Is there a standard notation for it?

Remark: given a finite $K\subset GL(n,\mathbb{Z})$, it is used to construct the crystallographic group in the arithmetic crystal class $(K,\mathbb{Z}^n)$ corresponding to the cocycle $\sigma$.