store function not finding the correct table

In my page I have a textbox where you can enter your name and a dropdown where you can select a group that your in. I also have 3 tables, the first table is the user table, then there is the groups table and the last one is called group_user table. The problem I'm having is that when I save it doesn't find the group_user table. Here is the error message

{"error":{"type":"Illuminate\\Database\\QueryException","message":"SQLSTATE[42S22]: Column not found: 1054 Unknown column 'group_id' in 'field list' (SQL: insert into `users` (`id`, `name`, `surname`, `email`, `group_id`, `password`, `updated_at`, `created_at`) values (, qq, qq, qq@qq.com, 1, y$foOlLh4ND8N190uOlMIJHuijtC6RCaj6yfWhQ1MS1sMkx.o2E\/pEe, 2014-11-26 08:25:13, 2014-11-26 08:25:13))","file":"\/Applications\/MAMP\/htdocs\/test-laravel\/vendor\/laravel\/framework\/src\/Illuminate\/Database\/Connection.php","line":555}}

Here is my controller

public function index()
    {
        setModuleSession("usersPermissions","");
        $usersList = \User::all();
        $group_options = \Groups::lists('name', 'id');
        return \View::make('admin.usersPermissions.index', compact('usersList'))->with('group_options', $group_options);
    }

public function store()
    {
        if(!empty($_POST) && \Request::ajax())
        {
            $user = new \User();
            $input = \Input::all();


            $validation = \Validator::make($input, \User::$rules); //nicole

            if($validation->fails()){
                $usersList = \User::all();
                $html =  \View::make('admin.users.partials.get-users-list', compact('usersList'))->render();
                return \Response::json(array('html' => $html, 'id' => $user->id, 'message' => ' User unsuccessfully saved.'));
            }

            if($validation->passes()){

                // Fields to ignore
                $ignore =   array('_token');

                foreach ($_POST as $key => $value) 
                {
                    if(!in_array($key, $ignore ))
                        $user->{$key} = $value;
                }

                $pw = $user->generatePassword();
                $user->password = \Hash::make($pw);

                // if(isset($_POST['group_id']))
                //  $user->groups()->sync(\Input::get("group_id", []));

                $data = array(
                    'name' => \Input::get('name'),
                    'email' => \Input::get('email'),
                    'password' => $pw,
                    );




                \Mail::send('emails.email', $data, function($message){
                    $message->to(\Input::get('email'), \Input::get('name'))->subject('Login Details');
                });




                if(isset($_POST['group_id']))
                    $user->groups()->sync(\Input::get("group_id", []));

                $user->save();
                //$user->create($input);




                $usersList = \User::all();
                $html =  \View::make('admin.users.partials.get-users-list', compact('usersList'))->render();
                return \Response::json(array('html' => $html, 'id' => $user->id, 'message' => ' User successfully saved.'));
            }
        }
    }

Here is my view

@extends ('admin.layouts.internal')
@section('title', 'Content > Manage users')
@section('template')
    {{ HTML::script("scripts/admin/modules/users.js") }}
    <h2 class="module-heading">Manage users</h2>   
    <div class="panel panel-default">
        <div class="panel-body">
            <button class="btn btn-afis-blue" onclick="showDiv('create');"><i class="fa fa-list"></i> create a new user</button>
            <div id="create" class="border" style="display:none;">
                <div class="white parent-target">
                    <button onclick="showDiv('create');" type="button" class="btn btn-danger btn-xs">cancel</button>
                    <br><br>
                    {{ Form::open(array('id'=>"user-frm", 'class'=>'modify-user-frm', 'url' => 'admin/users/manage')) }}
                        <p>
                            {{ Form::label(null, 'name') }}
                            {{ Form::text('name', null , array(
                                    'class' => 'input_text form-control',
                                    'placeholder' => 'name',
                                    'required' => true,
                                    'id' => 'name'
                                )) 
                            }}
                        </p>
                        <p>
                            {{ Form::label(null, 'surname') }}
                            {{ Form::text('surname', null , array(
                                    'class' => 'input_text form-control',
                                    'placeholder' => 'surname',
                                    'required' => true,
                                    'id' => 'surname'
                                )) 
                            }}
                        </p>
                        <p>
                            {{ Form::label(null, 'email') }}
                            {{ Form::text('email', null , array(
                                    'class' => 'input_text form-control',
                                    'placeholder' => 'email',
                                    'required' => true,
                                    'id' => 'email'
                                )) 
                            }}
                        </p>


                        {{ Form::label('group_id', 'Groups') }}
                        {{ Form::select('group_id', $group_options) }}

                        {{ Form::submit('SAVE', array(
                                'id' => 'submit',
                                'class' => 'btn btn-success submit-user'
                            )) 
                        }}

                    {{ Form::close() }}
                </div>
            </div>
            <br />
            <div id="page_list">       
                @include('admin.users.partials.get-users-list')
            </div>
        </div>
    </div>
    @if($errors->any())             
        {{ implode('', $errors->all('<p class="error">:message</p>')) }}
    @endif
@stop

Here is my model

<?php

use Illuminate\Auth\UserTrait;
use Illuminate\Auth\UserInterface;
use Illuminate\Auth\Reminders\RemindableTrait;
use Illuminate\Auth\Reminders\RemindableInterface;

class User extends Eloquent implements UserInterface, RemindableInterface {

    use UserTrait, RemindableTrait;


    /**
     * The database table used by the model.
     *
     * @var string
     */
    protected $table = 'users';

    public static $rules = array(
        'name' => 'required',
        'email' => 'required|email|unique:users'
        );

    public function groups()
    {
        return $this->belongsToMany("Groups")->withTimestamps();
    }

}

I always thought that

$user->groups()->sync(\Input::get("group_id", []));

would some how link the two tables and add the ids to the group_user table