There are researches which point out that social group diifferences affect school participation of children. However, it is important to understand, how these factors affect school participation.
In order to answer properly on your question research should be conducted. Aforementioned variables would have different effects in different societies.
Your question needs to be researched and based on clearly identified, measurable or observable categories for the two constructs you will be exploring. You can choose to study this quantitatively or qualitatively.
There is a lot of work already in this area, and so I would suggest a thorough read first. You may wish to start with some theoretical material in sociology: Marx, Durkheim, Bourdieu and Piketty come to mind; a proper sociologist would be able to advice you better here, but this would be a good start. Sociology of Education, Globalisaion Societies and Education and Critical Studies in Education are just some examples of excellent journals to look through, as they explore the very exciting touch points between sociology and education. In this way, you would be well advised to review recent empirical work in this area in the field of education, and I would recommend a 'Google Scholar' search using terms such as 'Social Mobility in Schools', or 'Intergeneralational Inequality', although the above journals might offer a more focused view, with a gurantee of quality peer-reviewed work.
Once you have a good idea of what the status quo is, then you might want to look into conducting some reseach of your own. You might also find your questions have been answered by then.
Read the making of the English Working Class (EP Thompson) and Bourdieu for a view on why the dominant education system often reproduces the same class system.
From experience and and a wide range of research id suggest looking at: quantity and quality of language in early years (lower socio-economic groups usually have a lot less words by age 4) and stress. If home is cold, scary, has no books or you haven’t had breakfast, you come to school tired, angry and not in a good place to learn. Lots and lots of research on that. EPPE studies are helpful. Good luck!
For example, students tend to gravitate to occupational areas that their parents/guardians or communities are involved in. My father owned a driving school as a young man and so we all grew up knowing good driving habits. Even though my brother after my attended the Queen's Royal College (top tier secondary school), he went to work for one of the top car sales companies in the country right after school (17 years). Today, he manages a top car brand for that company. His love for cars and successful career were no doubt due to my father's influence. Just a very practical example of how socio-economic and cultural differences among social group afffect the education of their children in their locality.
Where I live, in the interior of Brazil, this is a very problematic issue. There is a general perception, evidencied by many researches, that socio-economic conditions affect the education of children and adolescents in a variety of ways: either in the quality of schools (which are vastly different for the poor people and those who can afford education), in the students' living conditions, in the non-representativeness of their culture in the school curriculum, and even in the lack of perspectives for the future. Some research also shows that teachers acting differently in schools that serve the poorest people (with lower expectations), helping to maintain educational inequalities.
I have published some papers here in research gate about this issue, most of them are in portuguese but there are few in english. Maybe they help you to find out a way to answer your question in your own country and locality.