A popular Howard University student, whose stepfather was the leader of the failed coup in Trinidad, was beaten and then shot to death by Trinidad police after the rebels surrendered there this week, the student's grandmother said last night.

Njisane Omawale, 21, a senior finance major at Howard, was scheduled to be inducted as a national officer this week in the Alpha Phi Alpha fraternity.

Elaine Bailey, the grandmother, told a Newsday reporter that police came to her house near the capital, Port of Spain, Wednesday night and demanded that those inside come out.

Inside the house with her, she said, was Omawale, a girl, a young woman and Omawale's 54-year-old mother, Annisa Abu Bakr, the first of three current wives of Yasin Abu Bakr, the Moslem leader who led the six-day siege that claimed at least 22 lives.

She said police entered by forcing their way through a back door.

They grabbed Omawale, "beat him with a long black thing, like wire, and pulled down his pants."

Bailey said one police officer then kicked him down the stairs from the second floor to the ground floor and shot him several times.

"They came and shot him right on the spot," she said last night.

Attempts to confirm Omawale's death with officials in Trinidad by telephone were unsuccessful.

A spokesman for the Embassy of Trinidad and Tobago in Washington said he had no information about individual deaths on the island.

Members of Omawale's fraternity at Howard said yesterday that they had called the morgue in the capital, where an attendant described the body of a man who fit Omawale's description, including a brand of the fraternity's insignia on the left arm.

A cousin of Omawale's in New York said that Omawale's father, who is a Nigerian diplomat with the United Nations, had left Thailand, where he was working, to travel to Trinidad.

The whole family is angry, she said. "The government is not giving us any information."

Friends said Omawale rarely talked politics, but preferred to talk about studying business and law and activities in black fraternities.

They said they doubt that Omawale had been involved in the coup attempt. He returned to Trinidad every summer for about a month to visit his mother.

He was on the Dean's List at Howard every semester, friends said, and was active in the international students organization and the business students honor society. He was well known, students on campus said yesterday, especially among the more than 320 students from Trinidad who make up the largest contingent of foreign students from any one country.

His greatest love, his friends and cousin said, was for his fraternity.

Locally, Omawale was an officer with the Howard University chapter of Alpha Phi Alpha. He also served on the board of directors of the national governing group for black fraternities.

Omawale was to be installed this week as an assistant vice president at the fraternity's national convention in Miami. "He was scheduled to be here on Wednesday for his first board meeting," said Warren Scott, Alpha Phi Alpha's vice president for the Eastern Region.

Alonza Robertson, who joined the fraternity with Omawale in fall 1988, said he talked with Omawale by telephone on Tuesday. Omawale told him then that he was unable to get a flight back to the United States for the national convention.