In a city with an incurable fondness for putting labels on everything, it invariably is referred to as "the Greek lobby" or, when people are talking about its most active subgroup, as "the Gang of Four."

No one seems able to define just who and what it consists of or whether it even exists in a formal, organized sense. Yet, it's one of the toughest, most single-minded forces at work in the Washington political process.

Specifically, "Greek lobby" is a shorthand term for a loose array of individuals, organizations and ethnic interest groups united by one tie - their unyeilding opposition to President Carter's campaign for congressional repeal of the U.S. arms embargo against Turkey.

Three years ago, this coalition prodded Congress into imposing the embargo after Turkey used U.S. arms in its 1974 invasion of Cyprus, which has an 80 per cent Greek population.

Since then, as Turkey has continued to occupy roughly 38 percent of the island republic, the Greek lobby successfully has beaten back opposition to the arms ban from such heavy-weight adversaries for former secretary of state Henry A. Kissinger.

Now, it is preparing to meet Carter's challenge. And, as the House and Senate move toward expected votes on the embargo later this month, the administration is learning quite a bit about the Greek lobby's clout.

That the White House knows it's in for a big fight was underscored by its recent unveiling of an elaborate game plann to woo congressional votes. To kick off the campaign. Carter said he would make lifting the embargo his highest foreign policy priority and he opened his televised news conference last Wednesday by calling it "the most immediate and urgent foreign policy decision" facing Congress.

Still, now there are many in Congress who regard the White House's stretch drive as being too little and possibly too late. One strong advocate of repealing the embargo, Rep. Paul Findley (R-Ill.), says bluntly:

"It's not going to be enough for the president to make a few phone calls and have some congressmen over to the White House for breakfast. He's going to have to do a lot more - go on television and make other strong direct appeals to the American people."

"Otherwise," Findley warns, "Carter almost certainly will be courting disaster in the House and possibly in the Senate, too. The opposition is dedicated and strong, and it's been gearing up for this fight for a long time."

Despite the way that Findley and others describe the Greek lobby's power, it's not easy to pinpoint its sources of strength. For example, it doesn't counterpart on the American political scene - the Jewish community's Israeli lobby.

Last month, when Carter staked his prestige on a confrontation with the Israeli lobby over congressional approval of his plan to sell jet fighters to Saudi Arabia he won decisively.

On the surface, then, it would seem that the president, in a similar confrontation with the lesser-known Greek lobby, shouldn't have too much difficulty in convincing Congress to support him on another issue that he has described as being vital to U.S. security interests.

Yet, if Findley is correct, the impending showdown could see the House, at least, spurn Carter's appeal and repeat its action of a year ago when the last attempt to lift the embargo was made. At that time, the House rejected the repeal by 256-to-150.

The Greek lobby's ability to muster such lopsided tallies is a mystery to many political analyst who note that the wellspring of its power - the Greek-American community - is a relatively small ethnic group of 3 million people.

However, a closer examination shows that the Greek-American community has many of the attributes of the larger Jewish community and, like it, has been able to marshal its strengths for maximum political effectiveness.

For one thing, Greek-Americans are concentrated in a few urban, states - among them New York, Massachusetts, Illinois and Maryland - where they represent a sizable voting bloc in some congressional districts and can also effect the outcome of close state wide races.

In addition, they are economically and socially among the most successful of American ethnic groups, with substantial representation in business and the professions. They also tend to be substantial financial contributors to political campaigns, both Democratic and Republican.

Perhaps most importantly, the Greek community is one that has maintained its internal despite increasing dispersion from old ethnic neighborhoods to the suburbs. Cementing these bonds are such institutions as the Greek Orthodox Church and the fraternal organization, Ahepa, which keep Greek communities across the country in close contact with each other.

In their political affiliations, the Greek Americans tend to divide between Democrats and Republicans to a greater degree than other ethnic groups. But there is one issue on which community attitudes are unswervingly monolithic - an emotional loyalty to the Greek side in the complex Cyprus dispute.

And, if there is one thing that Greek Americans expect of their elected representatives, it's that they "vote right" on any question involving Greek-Turkish disagreements.

The community has a number of ways of transmitting this attitude to government officials, including such lobbying organizations as the American Hellenic Institute Public Affairs Committee.AHIPAC, which is noted for a combative, hard-line stance on Cyprus, is headed by Eugene Rossides, a former Columbia University football great who served as assistant secretary of the treasury under president Nixon and who is now a law partner of former secretary of state William P. Rogers.

But the community's most effective instrument for political action is the support it has built up within Congress itself. Essentially, on any issue involving Greek-American interests, the community knows it will get broad, bipartisan backing from urban-area legislators.

At the core of this congressional base is "the Gang of Four" - an outwardly unlikely, but highly savvy quartet of legislators who have evolved into the spokesmen and guardians of Greek-American interests on Capitol Hill.

All Democrats, the four are Reps. John Brademas (Ind.) and Benjamin S. Rosenthal (N.Y.) and Sens. Paul. S. Sarbanes (Md.) and Thomas F. Eagleton (Mo.). Each has been drawn into the partnership for different reasons.

Brademas and Sarbanes are Greek-Americans. Rosenthal has a very large Greek constituency in his congressional district. Eagleton, who is interested in questions of executive branch authority in foreign affairs, joined the group primarily because of philosophical differences with the executive over its alleged tolerance of Turkish actions in Cyprus.

All are adept practitioners of the infighting and horse-trading that are marks of congressional effectiveness. In Brademas, they have an especially valuable asset because of the power and prestige inherent in his post as majority whip, the third-ranking House Democratic leadership position.

In fact, Brademas already appears to have robbed the administration of the normally crucial leadership support in the impending arms embargo fight. Despite strong wooing by the White House, Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) has gone on record as opposing repeal of the embargo, and Majority Leader Jim Wright (D-Tex.) is, according to Findley, "securely in Brademas's pocket on this one."

The quartet has had similar success in lining up rank-and-file support in both houses. During last month's preliminary committee skirmishes, Carter's repeal request squeaked through the House International Relations Committee by a single vote, and it was turned down by the Senate Foreign Relations Committee - an action that will force the administration into the parliamentary pitfalls of trying to bring up the request on the Senate floor.

Nor has the quartet marshaled this support through simple arm-twisting and vote-trading. It also has been very effective in projecting an image of moderation and reasonableness for its position and in giving other legislators cogent arguments for voting against repeal.

In that area, the battle turns on the administration's contention that the embargo has failed to spur a Turkish withdrawal from Cyprus and threatens instead to undermine the western alliance's defenses in the Mediterranean by estranging Turkey from its NATO partners.

In response, the four are able to point out that, unlike the executive branch, they all strongly opposed the anti-Turkish military junta that ruled Greece from 1967 to 1974 and initially showed understanding of Turkey's argument that it invaded Cyprus to block a coup sponsored by the Greek junta.

Moreover, they are quick to add, they want Turkey to remain a strong and active member of NATO. Their support of the embargo, they say, is dictated solely by the continued Turkish occupation and they stress their willingness to life the arms ban as soon as Turkey begins removing its troops and negotiating a Cyprus settlement.

As an aide to Brademas sums it up: "If the Turks made a substantial withdrawal, John would probably rush onto the floor to sponsor legislation giving Turkey half of the U.S. defense budget and throwing in Jimmy Carter for good measure."

To the argument that the embargo has been ineffective, the four reply that neither the Ford nor the Carter administration ever seriously tried to enforce it.

"Two presidential administrations have turned their backs on the fact that Turkey used U.S. weapons for offensive purposes in violation of U.S. law," Brademas says. "Then, in clear defiance of the will of Congress, they allowed U.S. generals and U.S. embassadors in Ankara to tell the Turks not to worry - that they'd find some way of repealing or circumventing the embargo."

"There's this tendency to refer to us as 'the Greek lobby,'" he concludes. "I'd say a more accurate description of our position would be to call us 'the rule of law lobby.'"

It's a theme that he and his cohorts will be hammering at repeatedly in the days ahead, as the administration tries to chip away the embargo's congressional support by bringing such big guns as Secretary of State Cyrus R. Vance, Defense Secretary Harold Brown and the president himself to bear against wavering legislators.

At the moment, neither side seems willing to make any bets on the outcome. Bit most informed opinion on Capitol Hill seems to agree with Findley that the White House is clearly fighting an uphill battle and has a lot of work to do, particularly in the House, if it doesn't want to end up playing Goliath to the Greek lobby's David.