Should the Title of Co' have an Apostrophe?

The apostrophe is not wrong, but it is often omitted in company names like the one you quoted. In fact company names are not subject to the normal rules of grammar or punctuation.

It's right if the name is in reference to an electrical group possessed by Barclay. If the name was Barclays and the electrical group belonged to it then it would be "Barclays' Electrical Group." "Barclays Electrical Group" doesn't express possession.

Go to their website and see how they spell it. Also it depends on where you're referencing the name. If you're communicating some sort of published info, get it right. In a casual reference, spell it however you feel.

thank you