Gitlab API for all projects under group

You can also use the recently released Gitlab GraphQL API to query groups by name :

{
  group(fullPath: "your_group_here") {
    projects {
      nodes {
        name
        description
        httpUrlToRepo
        nameWithNamespace
        starCount
      }
    }
  }
}

You can go to the following URL : https://[your_gitlab_host]/-/graphql-explorer and past the above query

The Graphql endpoint is a POST on "https://$gitlab_url/api/graphql" An example using curl and jq:

gitlab_url=<your gitlab host>
access_token=<your access token>
group_name=<your group>

curl -s -H "Authorization: Bearer $access_token" \
     -H "Content-Type:application/json" \
     -d '{ 
          "query": "{ group(fullPath: \"'$group_name'\") { projects {nodes { name description httpUrlToRepo nameWithNamespace starCount}}}}"
      }' "https://$gitlab_url/api/graphql" | jq '.'

This is fairly handy if you use curl:

curl --header "PRIVATE-TOKEN: xxxxxxxxxxxxxxx" http://gitlab.your_namespace.com/api/v4/groups/your_group/projects

Adding to @Dante's answer,

This gives first 20 projects in the group.

curl --header "PRIVATE-TOKEN: xxxxxxxxxxxxxxx" https://gitlab.your_namespace.com/api/v4/groups/your_group_id/projects

To get more projects we should add 'page' and 'per_page' parameter.

The below request will fetch you up to 100 projects under requested group.

 curl --header "PRIVATE-TOKEN: xxxxxxxxxxxxxxx" https://gitlab.your_namespace.com/api/v4/groups/your_group_id/projects?&per_page=100" .  

If you now want all projects, you have to loop through the pages. Change the page parameter.

Add json_pp to your request to get a nicely formatted output.

curl --header "PRIVATE-TOKEN: xxxxxxxxxxxxxxx" https://gitlab.your_namespace.com/api/v4/groups/your_group_id/projects | json_pp