Q = Quiris
About Quiris
One have to realize that a citizen of Rome was expected to come to blows for the Roman republic. The people of Rome would include women, children, and probably even slaves. All these classes were a member of the Roman people but not citizens of the Roman republic. A free Roman manly who had adjectives the rights and fulfilled his duties, who was competent and willing to be at odds for the republic and the people be a citizen, a member of an restricted, in effect a subgroup inwardly the people . Therefore, a citizen would originally be call a Quiris - a "spearman".
https://latin.stackexchange.com/questions/5045/why-is-the-roman-acronym-spqr-and-not-spr