In a vote 70 days after the General election in February the Irish Republic has a minority government.
The above is a link to a post after that election detailing a different process on government formation. The fourth Monday after the vote the lower House of the Irish parliament meets to swear in the members and elect it’s speaker. The newly elected speaker puts the question to the House “who should the Irish President call upon to form a government?” Names comes from the floor and if they get 5% of the House (8) endorsements they get called upon to form a government-designate of 7 to 15 members. If there are more then 4 such nominated individuals the House then votes to endorse one candidate for Prime minister with the four with the most votes getting endorsed. Tuesday the nominated PM-designates are invited by the President to form a government. All of this is worked out even before Parliament meets. On Wednesday, 27 days after the election the Question is put to the House “Who does this House have confidence in to form a government of the Republic of Ireland?” The 2 councils with the least votes form shadow councils in the House. The top two go to a second ballot and the winner becomes the Council of Ministers in that Parliament and the runner up the Council of Opposition. Thursday the shadow councils are swore in before the House and on Sunday the Council of Opposition then the Council of Ministers is sworn in to office at Government House.
A government is in office for the duration of Parliament with no confidence motions. A minister may be dismissed at any time by a 60% majority vote with quorum. The Prime minister can be dismissed at any time by an absolute 60% majority (95). The House can trigger another government formation vote like the one at the start of each Parliament this takes an absolute two thirds majority vote (105). A new election happens ONLY by a motion of dissolution passed by an absolute three quarters majority vote (118).