Hurricane Alicia yesterday battered Houston and the Texas coast with 115-mph winds and sheets of rain that left at least six persons dead, 750,000 homes and businesses temporarily without electricity and millions of dollars in damage before it was downgraded to a tropical storm while moving farther up the state.

The season's first Atlantic hurricane spawned at least a dozen tornadoes, ruptured gas lines, downed electrical wires, upended an airport hangar and flooded low-lying areas.

More than two dozen Texas cities reported extensive damage from the storm, which moved ashore near Galveston about 2:30 a.m. EDT from the Gulf of Mexico and roared 50 miles northwest to Houston.

Downtown Houston was virtually closed off early yesterday as winds ripped windows out of skyscrapers, knocked over street signs and uprooted trees. One resident said it looked "like a war zone."

There were 65 arrests in Houston and Galveston last night for looting and 21 people in Galveston were arrested on curfew violations, law enforcement authorities said.

As the sun began to appear over Galveston in late afternoon, flash-flood warnings remained in effect in several counties in Texas and Louisiana. About 3 to 5 inches of rain had fallen by late afternoon, and the National Weather Service predicted more.

President Reagan ordered that all appropriate federal assistance be given residents involved in the cleanup, and was quoted by White House spokesman Larry Speakes as saying, "We deeply sympathize with the people of Galveston and south Texas who face this massive storm and stand to lose their homes and possessions."

Speakes said Reagan would consider a request from Texas Gov. Mark White to declare six counties hit hardest by the storm as disaster areas.

Houston Mayor Kathy Whitmire inspected the damage after the brunt of the storm passed through her city and called it "the most serious disaster I have ever seen." She predicted that it will take "a long time" for the city of 1.5 million to recover.

The Red Cross reported in Houston that about 42,000 persons had evacuated their homes before Hurricane Alicia arrived and that about 20,000 had taken refuge in 81 shelters over a 14-county area. But many other residents holed up in basements and other places, riding out the storm by candlelight.

Galveston was hit first. Just before the storm crashed ashore, 75 mph winds and tides lashed its sea wall, built after the hurricane that struck the island community in 1900, before the storms were given names, and eventually claimed 6,000 lives.

National Weather Service reconnaissance planes tracking Alicia said its sustained winds were clocked at 115 mph, with peak winds as high as 130 mph, as it blew across onto the mainland, pushing tides 12 feet above normal. In the 1900 disaster, tides were about 20 feet above normal.

The storm caused the interior wall of one Galveston hotel to crumble, ripped bricks and metal out of other buildings, cut power throughout the city of 60,000 and then headed toward Houston.

Civil Defense officials in Galveston said late yesterday that they had no estimate of damages but that they hope to complete an accounting today.

"Our damage estimate teams got out late because of the weather, and they don't have an estimate yet," city spokesman Judy Holland said.

Whitmire ordered downtown Houston barricaded about dawn as winds to 97 mph roared through the city, pockmarking with blown-out windows the modern skyscrapers that have sprouted along the city's main streets.

Winds ripped a skylight from the Hyatt Regency Hotel in downtown Houston, and hundreds of guests were routed from their beds as glass crashed 30 stories to the floor of the hotel's huge atrium.

As darkness fell, the downtown area was virtually deserted with police waving traffic away because of fallen glass. Other than the low rumble of a few passing cars, the only noise was the sound of broken glass being shoveled about in high-rise buildings.

Howard Armstrong of New York said the window in his 28th-floor room at the Hyatt shattered "like a bomb going off" about 5:45 a.m. He said he fled and returned at 4 p.m. to find the room and his belongings soaked from the torrential rain.

The eye of the hurricane settled over the city about 9 a.m., bringing an hour of relative calm despite heavy rains. Gretchen Huddleston, a Houston resident, said she used the time to inspect the damage in her neighborhood and found trees down and power lines strewn along one of the city's major thoroughfares.

"We kept seeing all these explosions outside and found out they were transformers from on top of the power lines blowing out," she said.

Damage was extensive throughout a 5,000-square-mile service area that includes Houston and other cities, according to Houston Power & Lighting Co. spokesman Steve Gonzalez.

Of 1.2 million customers, 750,000 were without power, and half of Houston's power lines were down, he said. By early evening power had been restored to about 350,000 customers, and emergency crews were heading into Houston to help repair the other damage.

Downed power lines and ruptured gas lines touched off fires in the Houston area, while the rains filled up bayous and created flooding.

One Civil Defense official reported looting in some parts of the city late in the day.

Hobby Airport south of the downtown remained closed throughout the afternoon, but some service was restored to the city's major airport, Houston Intercontinental.

Five of the deaths were in the Houston area, the sixth was in Dallas. Four were blamed on falling trees, authorities said, the body of a fifth victim was found in a flooded area and a sixth person was killed by a falling sign.

Alicia set off several false alarms at the Johnson Space Center in Houston, but the damage was slight and will not delay the scheduled Aug. 30 launch of the next space shuttle mission, officials said.

Small towns along the Gulf Coast reported flooding and blackouts throughout the day. Among those that reported power outages were Texas City, Fairchild, Thompson, Sugar Land, Stafford, Richmond, Pasadena, Baytown and League City. In addition, one unit in the Texas prison system reported loss of power.

Along the Houston Ship Channel, refineries and petrochemical plants were shut down, while workers along the channel, which runs from the city to the Gulf of Mexico, struggled to restrain several vessels that broke free during the height of the storm.

Meanwhile, the Coast Guard continued to search for three ships, including a tugboat with five persons aboard. The Coast Guard lost contact with the vessels several hours before Alicia hit land, but called the vessels as "unreported" rather than missing on the assumption that the problem was broken radio antennas.

As the hurricane lost strength over land, Weather Service officials downgraded Alicia to a tropical storm yesterday afternoon. At the time, it was in the Bryan-College Station area, north of Houston. Weather Service officials said it still bore gale-force winds and heavy rain toward Dallas.

Alicia was the byproduct of a Canadian cold front that moved through the eastern seaboard last week. The front stalled at the coast, but the collision of hot and cold air eventually created a thunderstorm that became Alicia.

Bob Sheets, a forecaster for the National Hurricane Center in Miami, was quoted by United Press International as saying the center expected "damage will be in the billion-dollar class." CAPTION: Pictures 1 and 2, with map, The Aftermath Of a Hurricane; Widespread destruction but remarkably low loss of life and personal injury are the marks left in Texas and Louisiana by Hurricane Alicia after it left the Gulf of Mexico and headed for Houston and the Texas interior. At Nassau Bay, the hurricane's winds and rain piled pleasure boats on a pier at a marina. Map shows the hurricane's path from the gulf to inland Texas, where its force diminished and the weather system was downgraded to a tropical storm. Boat cranes and other debris block a highway leading to the causeway to Galveston Island after the hurricane blew through the area. The hurricane is believed to be one of the most expensive in damages inflicted. Photos by AP, Map by Richard Furno--The Washington Post