Their name was the National Socialist German Workers’ Party, right? So, they must have been some kind of commie! Or so say some on the right.
The short answer is. Sort of. In the beginning. The Nazi Party did indeed have a left flank. in 1934, Hitler had them all killed in The Night of the Long Knives.
Nazi Party was anti-big business and anti-capitalist at first. The Strasser bothers represented the left flank. However, their anti-capitalism was a cover for hating Jews and taking their property and money. They perhaps supported the working class, but only if was Aryan.
In 1934 Hitler consolidated his power by having his opponents in and out of the party rounded up and murdered, including Gregor Strasser. Ernst Rohn, head of their paramilitary favored redistribution of the wealth and was killed too.
There is zero evidence that Hitler supported anti-big business or anti-capitalism. Having it was just an organizing ploy. After the Night of the Long Knives, the party dropped any even vaguely left positions and went full-on far right.