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Try this,

    $customerGroupsCollection = $objectManager->create('\Magento\Customer\Model\ResourceModel\Group\Collection');
    
    $customerGroupsCollection->addFieldToFilter('group_link',['eq'=>'thisisfreshgroup']);

    $collection = $customerGroupsCollection->getData();
    
    foreach ($collection as $value) {
       $customer_group_id[] = $value['customer_group_id'];
     }
    print_r($customer_group_id);