Many terrorist groups around the world throughout history have gone into politics. Many countries are born out of wars, with opposing sides moving into politics once the fighting is over. Many terrorist groups are connected to political parties while still involved in terrorism, and so having a political wing and a military wing. The political wing may negotiate and influence the military wing to give up their campaigns. A revolution can occur in a country, and once the revolution is over, the revolutionaries start to run the country and so enter politics. Many now well established and respected democratic political parties around the world were at one time involved in violence. Taking all those things into consideration, there are many potential answers for your question.
The Nazis are a political party in Germany in the 1930's through 1945. Invaded Poland and began WW11
First Jamat-i-islam is not an Islamic group but a political party. Government and many political parties expect them to be connected with international terrorist groups. Its mainly for political gain. But there are many of their deeds that were terrorist acts.
The Democratic Party
A political group is called a "party" or "political group"
The republican party was started in Wisconsin.
Political party
Narodnaya Volya, a terrorist organisation.
If the group of like minded people with regards to political opinions, they could form a political party. Most of the time, however, they can be describes as "public interest groups".
There is no group or political party called the "presidential party".
political party
A political faction is a group of people with a common political goal. This could be a group within a political party, or even a union.
democrats