Dallas — On the floor of the Republican convention here, the sea of red-cushioned chairs for the delegates is divided by blue-carpeted aisles. Amid all the noise and crowds, three-year-old Raegan Tennant sat happily in one of the aisles, holding a plastic American flag and wearing a tricornered colonial hat. On her pink dress were three buttons for President Reagan.
Her father, Massachusetts delegate Alexander Tennant, crouched in the aisle next to her. His daughter was not quite sure whose campaign buttons she was wearing. But her young father has been a Republican for four years, and, like many delegates who have come here for a nonsuspenseful week, he takes his politics quite seriously.
From the Alabama fireman who is spending about $1,300 to attend his first convention to the Hawaiian political consultant here for her sixth convention and who spends off-election years helping the homeless, there is a feeling of commitment among delegates here that is not at first evident in the swirl of noise and motion.
On the surface it looks like a giant party. The band plays so loudly you end up nearly shouting to someone next to you. The aisles are full of people.
Each state's delegation has a banner with the state name on it. West Virginia's banner had a handwritten note taped on it: ''Mary Lou - we love you, '' for Mary Lou Retton, the Olympics gold-medal winner in the all-around gymnastics competition. She is from West Virginia.
But on opening night this week, many delegates were trying to hear the speakers. And when Jeane Kirkpatrick, US ambassador to the United Nations, spoke , delegates were particularly attentive, some even requesting that reporters seeking interviews come back after the speech.
Mr. Tennant and his wife, Cynthia, an airlines flight attendant, exemplify Republican commitment. She has been elected to a party office in their hometown of Lynn, Mass. He is executive assistant for finance and administration for the Boston public schools.
When their daughter was born, says Mr. Tennant, ''we named her after the President,'' although they altered the spelling a bit.
''The ideas of competition, free enterprise, and individual initiative'' are what appeal to him most about the Republican Party. He is also concerned about the poor. But, he says, being a ''good manager'' is the best way to help the needy.
As one of the morning sessions of the convention was ending, alternate delegate Rick Harrison, a real estate agent from Minneapolis, was sitting in the Minnesota section, near the bandstand. He explained why he had come.
''I've had two ambitions in life: get elected to public office and go to a national convention. One down, one to go.''
He ran unsuccessfully for state representative in a district where Republicans are outnumbered 3 to 2. Getting here was not easy. He had to give a speech before state Republicans in his bid to be chosen.
''I got up and said I'm a right-winger and I want to go to the Reagan love-in in Dallas,'' he recalled.
Who are these delegates? What is their background?
Among the 4,473 delegates and alternates responding to a survey released here by the Republican Party:
* Males and females are almost exactly equal in number.
* Less than 4 percent are black.
* 80 percent are married.
* 45 percent have a college education and 22 percent went on to graduate school.
* 77 percent are veterans.
* 67 percent are Protestants; 23 percent Roman Catholics.
* 10 percent are retired; some 17 percent work in business or real estate and 11 percent in law.
* 18 percent are executives.
''I consider myself a liberal Republican,'' said alternate Ted Page, a prosecuting attorney in Crown Point, Ind. He was doing some paper work in a seat next to the telephone panel of his state's delegation. Each delegation can call someone on the Reagan-Bush campaign staff or someone at the Republican National Committee from the floor, in case he needs any last-minute advice on issues being voted on.
Attorney Page, 30, is feeling good about this convention. ''To be ahead (of the Democrats), have a popular President - one with a sense of humor, it's the last of the healing process after Watergate,'' he said, referring to the events that led to Richard Nixon's resignation. ''I was one of those who cried when Nixon resigned,'' he said.
Page came here because, he says, ''I wanted to see how Republicans operate on a national level. They have such a cold-business image.''
What he found here pleased him: ''They're nice, warm people.''
Across the floor, in Hawaii's section, Carla Coray said, ''I think we (Republicans) take a bum rap'' regarding the party's image as not being concerned with the poor. ''I'm moderate on social issues for the truly needy,'' she said, as another in a long line of speakers stepped onto the podium, high above the floor.
She is a lawyer and political consultant, but in off-election years she helps ''street people'' as a volunteer, collecting food for them. ''We don't do it because we're Republican, we do it because we care,'' she says.
This is Ms. Coray's sixth convention. She is her party's national committeewoman from Hawaii.
Some delegates here are ''people who have donated a lot of money (to the party) and are rewarded with a week of parties,'' she says. Many here have worked long and hard in their party, she adds.
''For the party person to be here is the highest honor,'' says Susan Heintz, a Michigan alternate. She was sitting in one of the sparsely attended mornings sessions where party business is addressed. The big-name speakers address the evening sessions.
Ms. Heintz was recently elected as a township supervisor in Northville, Mich. (pop. 14,000). She is one of an apparent minority here which finds the party platform too conservative on some points. She favors passage of the proposed Equal Rights Amendment to the Constitution, for example, something ruled out by the party's platform committee.
''There's a good future for moderate Republicans,'' Sen. Howard Baker (R) of Tennessee said to reporters as he stood, camera in hand, on the convention floor. Mr. Baker, a moderate himself, hopes so. He has indicated he wants to run for president in 1988.
North Carolina delegate John Cocklereece listened passively, wearing a button - ''Kemp in '88'' - for his choice, conservative US Rep. Jack Kemp of New York.