Coach Vince Dooley of fourth-ranked Georgia was looking for an invitation to the Sugar Bowl yesterday after the host Bulldogs downed Auburn, 24-13, clinching at least a share of the Southeastern Conference title.

"We deserve to be in the Sugar Bowl . . . We showed we were champions today," Dooley said after watching Buck Belue throw two scoring passes and all-America Herschel Walker rush for 165 yards, a touchdown and a Georgia single-season rushing record. Walker tied two other school records.

The Bulldogs' performance came before a crowd of 82,165, largest ever to see a sports event in the state.

It is the first time the Bulldogs have put together back-to-back SEC titles and perfect conference records. They will have to share the title with sixth-ranked Alabama if the Crimson Tide defeats Auburn Nov. 28; Georgia's last game is a nonconference contest with Georgia Tech.

The Bulldogs won the 1980 national championship with a 17-10 Sugar Bowl triumph over Notre Dame last Jan. 1. The Sugar Bowl selection committee is expected to meet Monday to decide whether it wants Georgia or Alabama, assuming the Tide defeats Auburn.

Sophomore Walker has 1,666 yards rushing --50 more than he had in 1980 when he set the NCAA freshman record and only 20 yards short of the Southeastern Conference single-season record.

Walker scored only one touchdown against the Tigers, but that was his 16th of the season and enabled him to tie Georgia records for most touchdowns in one season and most points in one season with 96.

Auburn (5-5, 2-3) got its touchdowns on a seven-yard run by Mike Edwards and a one-yard run by Clayton Beauford.