**Copy** `app/code/core/Mage/Adminhtml/Block/Catalog/Product/Edit/Tabs.php` **To** `app/code/local/Mage/Adminhtml/Block/Catalog/Product/Edit/Tabs.php`

You have to add your custom logic in method `_prepareLayout()` inside `foreach ($groupCollection as $group)` loop and skip that group whichever you want based on group id or group name and add that group tab in last or at your position.

**file content**

    <?php
    /**
     * Magento
     *
     * NOTICE OF LICENSE
     *
     * This source file is subject to the Open Software License (OSL 3.0)
     * that is bundled with this package in the file LICENSE.txt.
     * It is also available through the world-wide-web at this URL:
     * http://opensource.org/licenses/osl-3.0.php
     * If you did not receive a copy of the license and are unable to
     * obtain it through the world-wide-web, please send an email
     * to [email protected] so we can send you a copy immediately.
     *
     * DISCLAIMER
     *
     * Do not edit or add to this file if you wish to upgrade Magento to newer
     * versions in the future. If you wish to customize Magento for your
     * needs please refer to http://www.magentocommerce.com for more information.
     *
     * @category    Mage
     * @package     Mage_Adminhtml
     * @copyright   Copyright (c) 2014 Magento Inc. (http://www.magentocommerce.com)
     * @license     http://opensource.org/licenses/osl-3.0.php  Open Software License (OSL 3.0)
     */
    
    /**
     * admin product edit tabs
     *
     * @category   Mage
     * @package    Mage_Adminhtml
     * @author      Magento Core Team <[email protected]>
     */
    class Mage_Adminhtml_Block_Catalog_Product_Edit_Tabs extends Mage_Adminhtml_Block_Widget_Tabs
    {
        protected $_attributeTabBlock = 'adminhtml/catalog_product_edit_tab_attributes';
    
        public function __construct()
        {
            parent::__construct();
            $this->setId('product_info_tabs');
            $this->setDestElementId('product_edit_form');
            $this->setTitle(Mage::helper('catalog')->__('Product Information'));
        }
    
        protected function _prepareLayout()
        {
            $product = $this->getProduct();
    
            if (!($setId = $product->getAttributeSetId())) {
                $setId = $this->getRequest()->getParam('set', null);
            }
    
            if ($setId) {
                $groupCollection = Mage::getResourceModel('eav/entity_attribute_group_collection')
                    ->setAttributeSetFilter($setId)
                    ->setSortOrder()
                    ->load();
                $total=$groupCollection->count();
                $count=1;
                $last=null;
                foreach ($groupCollection as $group) {
                    if($count==$total)
                    {
                        $last=$group;
                        break;
                    }
                    $count++;
                    $attributes = $product->getAttributes($group->getId(), true);
                    // do not add groups without attributes
    
                    foreach ($attributes as $key => $attribute) {
                        if( !$attribute->getIsVisible() ) {
                            unset($attributes[$key]);
                        }
                    }
    
                    if (count($attributes)==0) {
                        continue;
                    }
    
                    $this->addTab('group_'.$group->getId(), array(
                        'label'     => Mage::helper('catalog')->__($group->getAttributeGroupName()),
                        'content'   => $this->_translateHtml($this->getLayout()->createBlock($this->getAttributeTabBlock(),
                            'adminhtml.catalog.product.edit.tab.attributes')->setGroup($group)
                                ->setGroupAttributes($attributes)
                                ->toHtml()),
                    ));
                }
    
                if (Mage::helper('core')->isModuleEnabled('Mage_CatalogInventory')) {
                    $this->addTab('inventory', array(
                        'label'     => Mage::helper('catalog')->__('Inventory'),
                        'content'   => $this->_translateHtml($this->getLayout()
                            ->createBlock('adminhtml/catalog_product_edit_tab_inventory')->toHtml()),
                    ));
                }
    
                /**
                 * Don't display website tab for single mode
                 */
                if (!Mage::app()->isSingleStoreMode()) {
                    $this->addTab('websites', array(
                        'label'     => Mage::helper('catalog')->__('Websites'),
                        'content'   => $this->_translateHtml($this->getLayout()
                            ->createBlock('adminhtml/catalog_product_edit_tab_websites')->toHtml()),
                    ));
                }
    
                $this->addTab('categories', array(
                    'label'     => Mage::helper('catalog')->__('Categories'),
                    'url'       => $this->getUrl('*/*/categories', array('_current' => true)),
                    'class'     => 'ajax',
                ));
    
                $this->addTab('related', array(
                    'label'     => Mage::helper('catalog')->__('Related Products'),
                    'url'       => $this->getUrl('*/*/related', array('_current' => true)),
                    'class'     => 'ajax',
                ));
    
                $this->addTab('upsell', array(
                    'label'     => Mage::helper('catalog')->__('Up-sells'),
                    'url'       => $this->getUrl('*/*/upsell', array('_current' => true)),
                    'class'     => 'ajax',
                ));
    
                $this->addTab('crosssell', array(
                    'label'     => Mage::helper('catalog')->__('Cross-sells'),
                    'url'       => $this->getUrl('*/*/crosssell', array('_current' => true)),
                    'class'     => 'ajax',
                ));
    
                $storeId = 0;
                if ($this->getRequest()->getParam('store')) {
                    $storeId = Mage::app()->getStore($this->getRequest()->getParam('store'))->getId();
                }
    
                $alertPriceAllow = Mage::getStoreConfig('catalog/productalert/allow_price');
                $alertStockAllow = Mage::getStoreConfig('catalog/productalert/allow_stock');
    
                if (($alertPriceAllow || $alertStockAllow) && !$product->isGrouped()) {
                    $this->addTab('productalert', array(
                        'label'     => Mage::helper('catalog')->__('Product Alerts'),
                        'content'   => $this->_translateHtml($this->getLayout()
                            ->createBlock('adminhtml/catalog_product_edit_tab_alerts', 'admin.alerts.products')->toHtml())
                    ));
                }
    
                if( $this->getRequest()->getParam('id', false) ) {
                    if (Mage::helper('catalog')->isModuleEnabled('Mage_Review')) {
                        if (Mage::getSingleton('admin/session')->isAllowed('admin/catalog/reviews_ratings')){
                            $this->addTab('reviews', array(
                                'label' => Mage::helper('catalog')->__('Product Reviews'),
                                'url'   => $this->getUrl('*/*/reviews', array('_current' => true)),
                                'class' => 'ajax',
                            ));
                        }
                    }
                    if (Mage::helper('catalog')->isModuleEnabled('Mage_Tag')) {
                        if (Mage::getSingleton('admin/session')->isAllowed('admin/catalog/tag')){
                            $this->addTab('tags', array(
                             'label'     => Mage::helper('catalog')->__('Product Tags'),
                             'url'   => $this->getUrl('*/*/tagGrid', array('_current' => true)),
                             'class' => 'ajax',
                            ));
    
                            $this->addTab('customers_tags', array(
                                'label'     => Mage::helper('catalog')->__('Customers Tagged Product'),
                                'url'   => $this->getUrl('*/*/tagCustomerGrid', array('_current' => true)),
                                'class' => 'ajax',
                            ));
                        }
                    }
    
                }
    
                /**
                 * Do not change this tab id
                 * @see Mage_Adminhtml_Block_Catalog_Product_Edit_Tabs_Configurable
                 * @see Mage_Bundle_Block_Adminhtml_Catalog_Product_Edit_Tabs
                 */
                if (!$product->isGrouped()) {
                    $this->addTab('customer_options', array(
                        'label' => Mage::helper('catalog')->__('Custom Options'),
                        'url'   => $this->getUrl('*/*/options', array('_current' => true)),
                        'class' => 'ajax',
                    ));
                }
    
                if($last)
                {
                    $attributes = $product->getAttributes($last->getId(), true);
                    // do not add groups without attributes
    
                    foreach ($attributes as $key => $attribute) {
                        if( !$attribute->getIsVisible() ) {
                            unset($attributes[$key]);
                        }
                    }
    
                    if (count($attributes)==0) {
                        continue;
                    }
    
                    $this->addTab('group_'.$last->getId(), array(
                        'label'     => Mage::helper('catalog')->__($last->getAttributeGroupName()),
                        'content'   => $this->_translateHtml($this->getLayout()->createBlock($this->getAttributeTabBlock(),
                            'adminhtml.catalog.product.edit.tab.attributes')->setGroup($last)
                                ->setGroupAttributes($attributes)
                                ->toHtml()),
                    ));
                }
    
            }
            else {
                $this->addTab('set', array(
                    'label'     => Mage::helper('catalog')->__('Settings'),
                    'content'   => $this->_translateHtml($this->getLayout()
                        ->createBlock('adminhtml/catalog_product_edit_tab_settings')->toHtml()),
                    'active'    => true
                ));
            }
            return parent::_prepareLayout();
        }
    
        /**
         * Retrive product object from object if not from registry
         *
         * @return Mage_Catalog_Model_Product
         */
        public function getProduct()
        {
            if (!($this->getData('product') instanceof Mage_Catalog_Model_Product)) {
                $this->setData('product', Mage::registry('product'));
            }
            return $this->getData('product');
        }
    
        /**
         * Getting attribute block name for tabs
         *
         * @return string
         */
        public function getAttributeTabBlock()
        {
            if (is_null(Mage::helper('adminhtml/catalog')->getAttributeTabBlock())) {
                return $this->_attributeTabBlock;
            }
            return Mage::helper('adminhtml/catalog')->getAttributeTabBlock();
        }
    
        public function setAttributeTabBlock($attributeTabBlock)
        {
            $this->_attributeTabBlock = $attributeTabBlock;
            return $this;
        }
    
        /**
         * Translate html content
         *
         * @param string $html
         * @return string
         */
        protected function _translateHtml($html)
        {
            Mage::getSingleton('core/translate_inline')->processResponseBody($html);
            return $html;
        }
    }