Summary: ``In this paper the network-type properties (network, $cs$-network, $cs^*$-network, $cn$-network and $ck$-network) of the space $\ssf{SP}^n_GX$ of $G$-permutation degree of $X$ are studied. It is proved that: \roster \item"(1)" If $X$ is a $T_1$-space that has a network of cardinality $\leq\kappa$, then $\ssf{SP}^n_GX$ has a network of cardinality $\leq\kappa$; \item"(2)" If $X$ is a $T_1$-space that has a $cs$-network (resp. $cs^*$-network) of cardinality $\leq\kappa$, then $\ssf{SP}^n_GX$ has a $cs$-network (resp. $cs^*$-network) of cardinality $\leq\kappa$; \item"(3)" If $X$ is a $T_1$-space that has a $cn$-network (resp. $ck$-network) of cardinality $\leq\kappa$, then $\ssf{SP}^n_GX$ has a $cn$-network (resp. $ck$-network) of cardinality $\leq\kappa$.'' \endroster