How does an “Independent Group” become an independent group?

Owl is confused.

The Local Government Independent Group website says:

“The Independent Group represents councillors in England and Wales who are Independent or of a political affiliation outside of Conservative, Labour and Liberal Democrat. It provides a voice at the national level and works within the cross-party Local Government Association (LGA) to ensure that the values and interests of its members are promoted.”

Who created the EDDC Independent Group? Who was invited to join? How did they elect their leader? What were people who joined told? Are they still independent if they include Tories in their Cabinet and as a committee chair? If EDA is “independent” according to the LGA what is different about EDCC?

Would really appreciate a tutorial!