Sharepoint 2013 Permission Management For Many Site Collections

Hi;

I have sharepoint farm like below topology.

1 Web Application

     10 Site Collections and too many site.

I created User Group on site collection and add users to group.And I use this group any sites on which created on site collection.

I must use this group different site collections.But I can not see this group another site collections.

Now I created this group manually all site collections but it's vey long and wrong way.And it very difficult manage permission.

How can I use this group another 9 site collection?Is there a way?

Thanks;

g:manav