This code snippets helps to create a new group in SharePoint site collection using PnP JS library

pnpjs.createspgrpoup.html

//Author: Shantha Kumar T
//Supports: SharePoint Online, SharePoint 2013+
//PnP JavaScript file available from https://github.com/OfficeDev/PnP-JS-Core
//More details: http://www.ktskumar.com/2016/09/pnp-js-core-create-sharepoint-group

<script type="text/javascript" src="/siteassets/scripts/fetch.js"></script> 
<script type="text/javascript" src="/siteassets/scripts/promise.min.js"></script> 
<script type="text/javascript" src="/siteassets/scripts/pnp.min.js"></script>
    
<div id="sample"></div>
    
<script type="text/javascript">
//The below PnP property used to create a new SharePoint Group
$pnp.sp.web.siteGroups.add({
    Title: "Group Name"
}).then(function(result) {
    var grpInfo = "";
    var grp = result.data;
    grpInfo += "SharePoint Group '<strong>" + grp.Title + "</strong>' created successfully!<br/>";
    grpInfo += "Below are some of the newly created group properties,<br/>";
    grpInfo += "Description :" + grp.Description; + "<br/>";
    grpInfo += "AllowMembersEditMembership: " + grp.AllowMembersEditMembership + "<br/>";
    grpInfo += "OnlyAllowMembersViewMembership: " + grp.OnlyAllowMembersViewMembership + "<br/>";
    grpInfo += "AllowRequestToJoinLeave: " + grp.AllowRequestToJoinLeave + "<br/>";
    grpInfo += "AutoAcceptRequestToJoinLeave: " + grp.AutoAcceptRequestToJoinLeave + "<br/>";
    grpInfo += "RequestToJoinLeaveEmailSetting: " + grp.RequestToJoinLeaveEmailSetting + "<br/>";
 
    document.getElementById("sample").innerHTML = grpInfo
});
</script>