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function IsCurrentUserMemberOfGroup(groupName, OnComplete) {
 
        var context = new SP.ClientContext.get_current();
        var currentWeb = context.get_web();
 
        var currentUser = context.get_web().get_currentUser();
        context.load(currentUser);
 
        var allGroups = currentWeb.get_siteGroups();
        context.load(allGroups);
 
        var group = allGroups.getByName(groupName);
        context.load(group);
        
        var groupUsers = group.get_users();
        context.load(groupUsers);
 
        context.executeQueryAsync(
                function(sender, args) {
                   var userInGroup = IsUserInGroup(currentUser,group);         
                   OnComplete(userInGroup);
                },
                function OnFailure(sender, args) {
                   OnComplete(false);
                }
        );
        
        function IsUserInGroup(user,group)
        {
            var groupUsers = group.get_users();
            var userInGroup = false;
            var groupUserEnumerator = groupUsers.getEnumerator();
            while (groupUserEnumerator.moveNext()) {
                var groupUser = groupUserEnumerator.get_current();
                if (groupUser.get_id() == user.get_id()) {
                    userInGroup = true;
                    break;
                }
            }
            return userInGroup;
        }
}

//Usage
function IsCurrentUserWithContributePerms() 
{
  IsCurrentUserMemberOfGroup("Members", function (isCurrentUserInGroup) {
    if(isCurrentUserInGroup)
    {
        // The current user is in the [Members] group
    }
  });

}
ExecuteOrDelayUntilScriptLoaded(IsCurrentUserWithContributePerms, 'SP.js');