A minority conservative group today won an unexpected election triumph over Spain's ruling center party in the rural northwestern area of Galicia, a traditional government stronghold.

Jubilant leaders of the Popular Alliance Party said after the election, held to select deputies to an autonomous Galician parliament, that the results had "changed the political face of Spain."

Popular Alliance tripled its vote in some areas, gaining 26 seats in the 71-member Galician assembly. The government party, the Union of the Democratic Center, which was estimated to have had its vote reduced by half, held 24 seats. The Socialist Party returned 17 deputies, and local nationalists won the remaining four.

The election is the first evidence of a significant swing to the right in Spain in the six years since the death of the late dictator Generalissimo Francisco Franco. It is also seen as a personal triumph for the authoritarian Popular Alliance leader, Manuel Fraga Iribarne, who heads a nine-member conservative minority in the 350-seat national Congress of Deputies in Madrid.

The result strengthened the call for center-right government alignment that has been issued consistently by Fraga, a veteran politician who served as Franco's tourism and information minister in the 1960s and was briefly interior minister after the dictator died.

As the final returns of Tuesday's poll were announced early today, Fraga said the result made possible "the profound reexamination of the relations between the political groups."

Spokesmen for the Union of the Democratic Center said the election hinged on the personal following Fraga enjoys in his native region, and claimed the Galician vote was a local one that would not be translated into national terms.

Popular Alliance spokesmen countered that Spanish Premier Leopoldo Calvo-Sotelo, who is also a native of Galicia, as well as senior members of the centrist Cabinet, had campaigned hectically in the region knowing full well the importance of the election.

Analysts here stressed that the swing to Popular Alliance had been considerable in the town centers of Galicia and that the centrists had been able to hold their ground only in the rural villages.

Galicia, an underdeveloped region that has seen many of its people leave to seek a better life, has been known for the practice of "Caciquismo," the system of vote organizing by local political bosses, and the Popular Alliance and other parties have charged that centrist govenment officials run Galicia like a private fiefdom.

The conservative Madrid newspaper ABC said in an editorial that the lesson of the Galician elections was that disenchanted centrist voters, seeking a change, had switched their allegiance, not to the Socialists, as had happened in Greece and France, but to the Popular Alliance Party.

National opinion polls at present put the Socialist Party, which opened its convention in Madrid today, as favorites to win general elections. Some analysts, however, claim that amid a climate of economic difficulties and political instability in Spain, the underlying mood is for law and order, as was evidenced in the Galicia election.

At the heart of the political debate within the Union of the Democratic Center, which has beaten the Socialists into second place in the two elections held since Franco's death, is the issue of whether the party should capture voters to its right or to its left.

The surprise election results in Galicia appeared certain to refire the center party's internal debate and strengthen the voice of those who seek a tactical alliance with Fraga's conservative group.

Calvo-Sotelo, who took office after February's abortive military coup, can constitutionally serve out the full four-year term until the spring of 1983 and he has publicly said that that is what he intends to do. But there is a growing lobby within the centrist party urging the premier to shift his policies toward the conservative vote and call a snap election early next year.

The Galician election sets up a government to administer local affairs, and was held in accordance with the new Spanish policy of autonomy for nationalist groups -- as with the Basque and Catalan assemblies -- within a unified country.

In the 1979 national elections, the centrists returned 17 congressmen from Galicia, as compared with six Socialists and only four from the Popular Alliance.