Let M denote the set of all real matrices of order $3 \times 3$ and let ${\rm{S}} = \{ - 3, - 2, - 1,1,2\} $. Let ${{\rm{S}}_1} = \left\{ {{\rm{A}} = \left[ {{a_{{\rm{ij}}}}} \right] \in {\rm{M}}:{\rm{A}} = {{\rm{A}}^{\rm{T}}}{\rm{ and }}{a_{{\rm{ij}}}} \in \;{\rm{S}},\forall {\rm{i}},{\rm{j}}} \right\},$
${{\rm{S}}_2} = \left\{ {{\rm{A}} = \left[ {{a_{{\rm{ij}}}}} \right] \in {\rm{M}}:{\rm{A}} = - {{\rm{A}}^{\rm{T}}}{\rm{ and }}{a_{{\rm{ij}}}} \in \;{\rm{S}},\forall {\rm{i}},{\rm{j}}} \right\},$
${{\rm{S}}_3} = \left\{ {{\rm{A}} = \left[ {{a_{{\rm{ij}}}}} \right] \in {\rm{M}}:{a_{11}} + {a_{22}} + {a_{33}} = 0{\rm{ and }}{a_{{\rm{ij}}}} \in \;{\rm{S}},\forall {\rm{i}},{\rm{j}}} \right\}.$
If $n\left( {{S_1} \cup {S_2} \cup {S_3}} \right) = 125\alpha $, then $\alpha$ equals _____.