Is there a measure of social inequality?

Question

A measure of economic inequality in a population is the gini coefficient.
Is there such a measure of social inequality as well?

The social rights include labor market, the source of income, health care, and freedom of speech, education, (political) representation, and participation (Source of definition). These rights vary among different strata of the society- and thus we have phenomena like racism, sexism, casteism and several other types of discrimination which restrict specific people from having various social rights. This is what we term as social inequality.
Is there a metric to quantify social inequality?

I'm interested in comparing the state of social inequality between countries, and over time within the same country. The issue with measures like HDI is that they do not measure inequality specifically.

Answer 1

The matter is still largely unsettled, namely, there is not a broad consensus on how to measure it.

Lookup

Binelli, C., Loveless, M., & Whitefield, S. (2015). What is social inequality and why does it matter? Evidence from Central and Eastern Europe. World Development, 70, 239-248, https://www.researchgate.net/publication/273061839_What_Is_Social_Inequality_and_Why_Does_it_Matter_Evidence_from_Central_and_Eastern_Europe

and (older)

Pandey, M. D., & Nathwani, J. S. (1996). Measurement of Socio-Economic Inequality Using the Life-Quality Index. Social Indicators Research, 39(2), 187–202. http://www.jstor.org/stable/27522951