$siteId = Craft::$app->sites->getPrimarySite()->id;

$group = new CategoryGroup([
    'name' => 'Test Category Group',
    'handle' => 'testCategoryGroup'
]);

$siteSettings = new CategoryGroup_SiteSettings([
    'siteId' => $siteId,
]);

$group->setSiteSettings(array($siteId => $siteSettings));

if (!Craft::$app->getCategories()->saveGroup($group)) {
    var_dump($group->getErrors());

    exit();
}

Craft::$app->getSession()->setNotice(Craft::t('app', 'Category group saved: ' . $groupName));