The variables for that trigger are as follows.
Code:
$_PLUGINS->trigger( 'gj_onAfterUpdateGroup', array( $this, $old ) );
You can find trigger variables in the below documentation.
www.joomlapolis.com/documentation/279-community-builder/tutorials/18358-using-cb-triggers
Variables are access in CB Auto Actions incrementally starting from 1. In this case var1 is the group object after it has been updated and var2 is the group object before it has been updated. You can use substitutions against these variables. So for example [var1_name] is the group name and [var1_id] is the group id. It will navigate into parameter objects as well so you should be able to use [var1_params_gj_custom] to access your parameter value entirely through substitutions.