How to Create a New Site Group Programmatically

Steps

• Open Visual Studio in your system
• Select Console Applciation template and give as name .
• Add a Microsoft.Cleint Assembly refrence file in right side refrence tab in visual studio.
• Replace Program.cs with the source code  

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using Microsoft.SharePoint.Client;
using System.IO;

namespace CSOMCodeSamples
{
   class Program
   {
      static void Main(string[] args)
      {

         // ClientContext - Get the context for the SharePoint Site

         ClientContext clientContext = new ClientContext("http://gauti.sharepoint.com/sites/CSOM/");
         // Get the SharePoint web
         Web web = clientContext.Web;

         // Get all the site groups
         GroupCollection groupColl = web.SiteGroups;

         // Create a new site group
         GroupCreationInformation creationInfo = new GroupCreationInformation();
         creationInfo.Title = "gautiGroup";
         creationInfo.Description = "Custom group created using CSOM";
         Group newGroup = groupColl.Add(creationInfo);
         clientContext.Load(newGroup);
         // Execute the query to the server
         clientContext.ExecuteQuery();
         // Display the newly created group name
         Console.WriteLine(newGroup.Title + " is created successfully");
         Console.ReadLine();
      }
   }
}

Hit f5 and check the out put in SharePoint group created successfully.