It is the Establishment school of Southern California, the university that is supposed to produce football players, pharmacists, astronauts and White House aides in Republican administrations.

It is USC, the School of Tailbacks named Mike Barrett, O. J. Simpson, Clarence Davis, Anthony Davis, Ricky Bell and, now, Charles White. It is buttons proclaiming "God is a Trojan" and "Don't Toy With Troy."

It is the University of Southern California, headed casually for its 10th Rose Bowl in 14 years and a chance at its ninth national football championship.

On the sun-drenched central USC campus near downtown Los Angeles, Vance I. Peterson, football fan and academic relations director, recently thus summarized the way outsiders see USC:

"We have these images of being a fraternity school for rich kids, a football factory, a place where the scions of the Southern California rich come who are all white and blond and blue-eyed and lived in San Marino," Peterson said. "All these images persist about this place and in every case I defy people to provide the data that will prove their point. But images die hard."

In fact, a case could be made that USC is the most cosmopolitan of western universities, with a wider diversity of courses and student body than any of its alternatives. Its domestic minority enrollment (23 percent) and its foreign enrollment (11 percent) are greater than at any of the University of California campuses. Half the USC students receive grants in aid, and remedial reading, speed reading or tutoring is available to any freshman.

When he came here from Stanford two years ago, Peterson believed most of what he now considers myth about USC. But now, along with nearly everyone else at this prideful school, Peterson can talk for hours about the lesser known USC where a $24 million cancer research center is under construction and where the nation's first university-based institute for the study of hydrocarbons opened this month.

It is a USC that has leaped from 34th to 19th among the country's universities in federally sponsored research, outstripping in some years such prestigios schools as Yale and the University of Chicago. It is a USC that now boasts top schools of law, dentristry, music, arts, filmmaking, journalism, the Laffer Curve and such recruiting fillips as a tenfold increase in the number of national merit finalists in the engineering school.

But the old USC still flourishes with a vengeance on the football field -- to the delight of every Trojan. If anything, it has become more important than before.

As UscY has reached out to enroll students from the black communities of Compton and Watts and the Mexican-American communites of East Los Angeles and Montebello, the university's successful athletic program -- a national record of 63 intercollegiate athletic championships -- has been an important recruiting tool. At the pinnacle of that success is the football team.

Outside the university, USC football is an important focus for sprawling, rootless Southern California. If intercollegiate football were abolished, Ohio State would still be the biggest thing going in Columbus. Austin is the state capital of Texas and Berkely and Tuscalosa have traditions, however faded, that transcend football.

But Southern California, as Charles A. Stoddard wrote in 1894, "is made up of groups who often live in isolated communities, continuing their own customs, language and religious habits and associations." Historian Carey McWilliams, writing 52 years later, called the region "an archipelago of social and ethnic but culturally disperate."

In this milieu, in this largest city of the western world that has no opera company of its own, sports is the great unifier, the one common interest other than the weather and perhaps Hollywood.And the great sports teams of Los Angeles, in terms of this type of interest, are the Los Angeles Dodgers and the USC Trojans, the only college football team in the United States that consistently outdraws a professional team playing in the same facility.

"We grew up talking about O. J. and Ricky and we wanted to be like Charley White," said a black USC liberal arts major who says he is "too slow" to be an athlete. "I go to all the games. Charles and Marcus (Allen the fullback who is scheduled to be the USC tailback in 1980) are important to me."

All the great USC tailbacks of modern times have been black. Hispanics are the largest minority group in Southern California but the, says George Pa, a Mexican-American graduate of USC, have been stereotyped as being "small but slow."

This year, however, tackle Anthony Munoz seemed an even surer bet than White to be All-America until he was injured in USC's first game. Danny Garcia stayed healthy and became one of the Pacific Coast's best pass-catching ends.

Pla, and officials in the administration of Gov. Edmund G. (Jerry) Brown Jr. before resigning to become executive vice president of the Mexican-American community organization known as IELACU, remebers being lonelier than the Lonely End of Army football fame while a student at USC five years ago. In 1974 he was the only Mexican-American to graduate from the USC school of business administration, where 136 Mexican-Americans are now enrolled. Pla, a booster of Trojan football, heads a committee that has raised $500,000 and provided more than 500 academic scholarship for Mexican-Americans at USC during the last five years. USC has matched the comittee's money 2-1.

Not that it is all happiness and hot tubs at USC.

The black liberal arts major who says he is too slow for intercollegiate athletics complains of "an almost racism" on the part of some students and professors, "a kind of holding back that said to me they didn't think I belonged here." He adds that he was quickly accepted once he demonstrated he was a high-quality student.

A woman employe of the university makes a similar point. She did well in her work but found what she calls a "honey syndrome" -- is if some of the older faculty didn't understand that a woman could be a professional instead of "honey." But she was promoted and has done well at the university, which she says is "so success-oriented it will value anyone who can perform or achieve."

USC unabashedly uses the success of its athletic teams, particularly football, to attract students, faculity and alumni dollars. Then it turns around and uses its growing academic prestige to convince black athletes at San Fernando High (home school of Anthony Davis and Charles White) that they will get a firt-rate education if they become Trojans.

In effect, USC promises more by promising less. Ricky Bell, now one of professional football's premier running backs at Tampa Bay, has been quoted as saying that he turned down money and cars from other schools for simply the chance to play at USC. Clarence Davis has recalled that he was promised nothing, and liked it. But every athlete from a low-income family, particularly if he is a ball-carrier, knows that he will have national television exposure and a healthy pro contract if he succeeds as a football player at USC.

Success on the football field was not enought for John McKay, USC's football coach from 1960 through 1975 and now coach at Tampa Bay. He wanted his star players, particularly his tailbacks, to be role models for those who would come after them and successful achievers in their own right -- people who took care of their families, invested their money, used their athletic talents as a bridge to other successors.

While he could be a distant figure -- O.J. Simpson has recalled being "frightened" by him -- McKay installed a prideful quality of organization in his teams reminiscent, say, of the New York Yankees of two generations ago or of the Boston Celtics in the Bill Russell era. It was a pride which said that merely being part of the team was something special.

McKay's successor John Robinson has, if anything, done more.

Robinson is, in the words of USC's senior quarterback Paul McDonald (who boasts a 4.6 grade-point average) "a unique combination of intellectualism and emotionalism." He is a coach who takes inordinate pride in the return of Bell to USC last year to graduate and in the personal development of White under the tutelage of ex-marine backfield coach John Jackson, a black.

As Robinson puts it, White came into the university "thinking of Charley White" and talking cockily of winning two or three Heisman trophies. The cockiness was disabused in an early practice session with All-America tackle Gary Jeter, who followed a USC tradition of welcoming star halfbacks to the collegiate equivalent of the NFL.

In the four intervening years, White has emerged as a personable and polished young man who credits the offensive line for his achievements and talks of a career in broadcasting. White, says Robinson, "no longer is one-dimensional."

Making athletes multidimensional has become something of an obsession with Robinson. He recalls a conversation a few years ago with his friend John Underwood, the Sports Illustrated writer, in which Underwood argued that making leaders and students out of athletes was a coach's responsibility, particularly at highly visible USC.

"You can go through four years of college and be oblivious to everything that goes on and come out of it being nothing other than what you were," Robinson says.

"in fact, people have done it and our system in some ways over the last 15 years has allowed that to happen -- and that's a disgrace, a pure disgrace. It's somewhat racial, because the black athlete has been most successful and a higher percentage of blacks are deprived of normal educational opportunity in the grammer schools and high schools." . . . . . .

Robinson's consciousness of the importance of reading was heightened by an experience in his own family. The 44-year-old coach is married to a USC teacher of music and voice and they have four children, one of them a daughter with dyslexia.

"She was reading at third-grade level at 10th grade and begining to think she was stupid," Robinson recalls. "She was beginning to accept those things. Everything artistic or everything that didn't require reading said, "This girl's not stupid.' That got me hooked and wondering, damn, how many people are in this position and are tuning out or turning off because of this or some insecurity they have.

"So we've tried hard when we bring a freshman in -- all freshman -- to offer a speed reading course or remedial reading. We test them as much as we can, we sit down with them and say 'you're really lousy in reading, let's teach you to read and you take care of the classes.' It's the same thing in football. We say, 'you're not very strong, you've got to lift weights.' There's a simple solution for the problems we face on the football field. There ought to be a corresponding academic responsibility."

Robinson, who thinks of himself as a teacher as much as a football coach, also has tried to win the hearts and minds of the USC faculty.

A biology instructor who is one of his converts recalls that he thought Robinson "was just giving the faculty a snow job" when he told them he wanted football players who were motivated to graduate. Now, the biologist is a regular attendee at the seminars Robinson holds once a week during the football season for faculty members.

On the Wednesday before Thanksgiving Thursday and UCLA game Saturday, the first question to Robinson is, "Why is our pass defense as porous at the end of the season as it was at the beginning ?" Robinson jokes with the professor who asked the question and uses it as a launching pad for a concise, literate and moderately technical discussion of college football defenses.

What seems to have sold the USC faculty more than anything else is the practiced humility of university athletic presentatives, who say repeatedly that football is the mean to a more important goal. The best expression comes from USC Athletic Dirctor Richard H. Perry:

"When I attended the groundbreaking ceremonies for the new cancer research center, there were maybe 150 people there. And I found it appalling that 100,000 people will come to the Rose Bowl to watch us play Ohio State . . . In terms of honest values, whether we win that game or lose that game isn't going to impact the world we live in a whole lot. Nothing really serious is going to happen. But, my God, if you've just been told you've got cancer, that research center becomes pretty important. Hopefully, over football program provides us an avenue to remind people of that."

It is more an arena than an avenue. On any given football Saturday at USC there are eight or nine fund-raising luncheons. The different professional schools maintain regular groups of contributing associaes whose social focus is the football games. At the apex is the president's reception, with an open bar and elegant buffet before the game and drinks and sandwiches afterward while the parking lots clear. The invitees are rich alumni and prospective donors with a sprinkling of politicians and selected press. And the message, though civilized and softly sold, is unmistakable -- USC needs money for its growth, expansion and success.

On UCLA Saturday, the introduced guest is one Robert Allison Seale, a graduate of Boy's Town and a creator and marketer of educational programs who has just pledged $1 million to USC's College of Continuining Education. Seale has brought with him the Boy's Town Choir, which sings the "USC Fight Song" and "He's Not Heavy, He's My Brother" for an appreciative audience.

The choir and the well-heeled alumni then trot off towatch a football game that makes up for in decisiveness what it lacks in excitement. The biggest USC mishap of the day comes early when the rider of Traveler III, the university's perennial white charger, falls off his horse. UCLA also is quickly unhorsed, trailing 35-0 at halftine, and eventually losing, 49-14. The USC fans take it in their stride except for a vendor who is peddling "Happiness if Going to the Rose Bowl" buttons. He tries hard but does not sell out. Of course, USC is going to the Rose Bowl to play unbeaten Ohio State. What else would the Trojans be doing New Year's Day?