It really depends. If the "a group" is everybody that is legally allowed to vote, and they all vote directly for the course the government should take, then yes, it is direct democracy.
However, taking a "vote on something" is rather vague. The United State's political system has people vote, but it is mostly indirect democracy, in that they vote for representatives of their own values who would voice those opinions in the government.
Direct democracy implies that each individual gets a voice in the government directly, and could really be defined as populist ruling, in which the people have their views met by directly influencing the laws of the country.
~
