If there is any one center to the persisting struggle between black and white nationalism in South Africa today, it is undoubtedly here in this sprawl of brick and wooden matchbox houses where the "children's revolution" of this nation's frustrated black population draws its recruits.

Since the first outbreak of protest here in June 1976, militant students have succeeded in creating a deadlock with the white establishment, forcing the collapse of the township council and replacing it with their own shadowy body while blocking all government attempts to establish an appointed leadership.

Without question, the government's drastic measures this week to outlaw 17 black organizations, ban two black publication and arrest 40 or more black leaders was partly, and perhaps even primarily, motivated by the impasse here in Soweto which it fears may spread to black townships elsewhere.

At the heart of the current crisis is the same issue that triggered the first unrest 16 months ago - "Bantu education," the separate and unequal system of schooling for some 4 million black youths throughout the country. But it has now taken on much larger dimensions.

Since early August, thousands of high school students under the highly secretive and effective leadership of the now banned Soweto Students' Representative Council have been boycotting classes in protest as much against the country's whole system of apartheid, or strict racial segregation, as against Bantu education itself.

At first, the strike was largerly confined to Soweto's 27,000 high school students. Little by little, it has encompassed at least 200,000 students and primary school pupils in a growing number of towns and cities across the country and even in the normally tranquil rural black homelands.

Here in Soweto, some 500 teachers and principals have also joined the boycott, although 122 of them recently had second thoughts and withdrew their tendered resignations.

Far more dramatic is the spread of the strike to primary school here and in other cities through the persuasion, and sometimes use of force, by high school students, who seem more determined than ever to challenge the government following last week's bannings and arrests.

"We are shocked and angered by this," said one Soweto resident who added: "Now that all our organizations have been banned we have no alternative but the NAC and the PAC."

The African National Congress and the Pan-Africanist Congress are the two oldest black nationalist organizations, banned in the early 1960s. Both are based abroad and dedicated to overthrowing the white South African government through armed revolution.

Neither group was originally behind the Soweto unrest the began in June, 1976 over the issue of the use of Afrikaners. They have capitalized on the continuing student protest movement, however, and are using the growing number of fleeting youths to build guerrilla armies in camps in Tanzania, Angola and other black-ruled African countries.

Precisely how many students are on strike throughout South Africa is impossible to tell. Their numbers seem to be growing daily. However, the boycott has still not caught on in the port city of Durban, is being followed only sporadically in the country's other main city, Cape Town, and has a long way to go yet before it encompasses the entire black school population.

Student and teacher strike leaders blame their difficulties in the Durban area primarily on the chief minister of Kwazuland, Gatsha Buthelezi, whose Inkatha Movement has so far refused to support the strike.

They also point to the sheer size of the country.

"We are having trouble with communications," said one activist who was involved in getting teachers to join the strike before his arrest Wednesday. "But we are determined to continue even if it takes years to get rid of Bantu education. We will not stop."

He noted that the black students in neighboring Mozambique had boycotted schools for as long as seven years during the nationalist struggle for independence from Portuguese colonial rule. "We can do the same thing there if we have to," he said.

This activist made it clear that the issue of Bantu education was being used by the students as a wedge to split the whole apartheid structure.

"The problem does not stop for us at the schoolhouse gate, you know. It's jobs and everything."

The controversy over Bantu education has been simmering for years without the government's taking any action to deflate it.

The demand of the black power and consciousness movement has not been mainly for a separate black studies program as in the United States but just the opposite - the integration of so-called Bantu education into the white system to insure the same level and standards.

For the black militants. Bantu education has always meant, as one of them put it, "Second-class schooling for people regarded as second-class citizens expected to get only seconds class jobs in their lives."

The statistics of the crisis over black education explain many of the complaints being aired these days. First of all, in the past 25 years there has been of fivefold increase in the number of Africans attending school to about 4.25 million.

The government tried to deal with the problem through double sessions at each school with teaching time reduced from 4 1/2 hours to three. Much of this reduced time was taken up with learning three languages - English, Afrikaans and that of the pupil's own ethnic group.

In addition, the drop-out rate among blacks is staggering. By the fourth year of schooling, 46 per cent of them have left the classroom, by the sixth year, 65 per cent and by the 12th grade only 2 per cent are still there, according to Franz Auerbach, a leading white educator. By contrast 58 per cent of the white students who start school are still in school in the 12th grade.

A comparison of the government expenditure per pupil is equally telling. In 1975, it stood at 644 rand ($740) for whites, 140 rand for "coloreds" (persons of mixed marriages), and 42 rand for blacks. While the increase in the outlay for white education was fivefold between 1953 and 1975, it was half as much for blacks, according to Auerbach.

Another student complaint has been the low level of qualifications of many of their teachers. Nearly half of the 78.000 black instructors have only 10 years of regular schooling and a two-year course in teaching. About 15 per cent of them rate as "totally unqualified," in Auerbach's view.

In the past 16 months, the government has taken a number of steps to meet the student's demands for better education and other changes. For instance, each school is now allowed to choose the language of instruction it prefers: 2,600 of the 4,500 teachers in Soweto are getting high school degrees at government cost and being given bonuses if they continue beyond that; free books and better facilities are being provided or built, and the word "Bantu" will soon be dropped from the government's vocabulary.

There is even talk, finally, of scrapping the Department of Bantu Education and integrating it into the ministry that deals with white education, although schooling would still be separate for the two races.

As for the quality of what is taught officials at the Department of Bantu Education insist that the currculum has always been the same for all races and that it is the teachers who are responsible for chosing which books they use in class - as long as they are taken from a government-approved list.

They also insist that the government has shown its clear intention of reforming black education now and that the issue is no longer a purely educational one

"It has become an emotional issue that has been misused because of political reasons in order to create chaos," charges the Bantu education office for Soweto. "It is doubtful whether a solution of this checkmate situation will be found by educationalists."