Find the name of a CNContact's group (CNGroupName)

So I only recently uncovered the Contacts Framework through this video. As such I’m not yet accustomed to the API. Basically my main problem is that I can’t seem to find a way to access the name of the group a CNContact is in. The only support I can find is in Apple’s own documentation, which isn’t very helpful.
if someone could point me in the right direction towards how to fetch the group name, I would be very grateful.
My code is below,

//  ModelData.swift
//  B-Day

import Foundation
import Contacts
import SwiftUI

 struct Contact: Identifiable {
     let id = UUID()
     let category: String
     let firstName: String
     let lastName: String
     let birthday: DateComponents?

 func fetchAllContacts() async -> [Contact] {
    var contacts = [Contact]()
    let store = CNContactStore()
    let keys = [CNContactGivenNameKey, CNContactFamilyNameKey, CNContactBirthdayKey, CNContactIdentifierKey, CNGroupNameKey] as [CNKeyDescriptor]
    let fetchRequest = CNContactFetchRequest (keysToFetch: keys)
    do {
        try store.enumerateContacts(with: fetchRequest, usingBlock: { contact, result in
    //this should fetch the name of the contact's group
            contacts.append(Contact(category: contact.groupName, firstName: contact.givenName, lastName: contact.familyName, birthday: contact.birthday))
    catch {
    return contacts