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single_cat_title(); 
single_tag_title();
the_archive_description();

$term = get_term_by( 'slug', get_query_var( 'term' ), get_query_var( 'taxonomy' ) ); 
echo $term->term_group;

You can use it for the all of the following values:

term_id
name
slug
term_group
term_taxonomy_id
taxonomy
description
parent
count