Ethnikos Gymnastikos Syllogos

Before 1908 football at the Olympic Games was merely an exhibition, played, if at all, between
club sides. The decision of the IOC to retrospectively publish 'medal tables' based on the outcome of these matches is frankly absurd.
The attempts to include football at the 1906 Intercalated Games offered no real encouragement for the prospects of a meaningful international tournament developing. On their foundation in 1904 FIFA had stated  their intention to introduce an international tournament in 1906, but nothing came of it.
What the 1906 tournament did give us though is the first seeds of a Greek national team. 
The Thessaloniki selection was largely made up of ethnic Greeks, but the Athens selection, effectively Ethnikos Gymnastikos Syllogos, is the team from which the 2004 European Champions  trace their descent. 
Ethnikos Gymnastikos Syllogos were primarily a gymnastic squad, and they had participated in the 1896 Olympics. At the time Greek football had no independent governing body. Football, along with other sports, was administered by the Hellenic Gymnastic Federation. 
The only non- Ethnikos Gymnastikos Syllogos member of the Athens selection was Georgios Kalafatis of Panellinios Gymnastikos Syllogos.  Kalafatis later founded Panathinaikos and coached the Greek team in their first official international at the 1920 Olympics.
Sadly Ethnikos Gymnastikos Syllogos did not display the sort of sportsmanship that one associates with the Olympic ideal. 9-0 down to Denmark at half time in the final, they refused to take the field for the second half, and were promptly expelled from the tournament.