>Do you agree with the observation every fascistic regime is really an alliance between the titans of industry and the financial elite and politicians they support?

It depends on what you mean by 'alliance'. I don't think Nazi Germany, for instance, was really allies with German industrialists and financiers; certain industrialists and financiers were Nazis, but most of them just went with the prevailing wind, and the Nazis continued to allow them to exist as long as their business served the state.

>If so, how does it explain the traction it has among the lower classes?

Typically because a fascist regime will project the importance of the lower classes (in Nazi terms, the 'Volk'), and will often promise to address their problems ('full employment'), but this doesn't mean they necessarily gain a lot of traction with the lower classes, nor that they do anything about lower class problems, or if they do, that they then won't add a new raft of problems. The Nazis were never that popular among the working class. Nazism was a solidly middle class movement.