BuddyPress.org

The reason is bp_get_group_avatar_thumb() assumes you are inside group loop and simply ignores the $group,which you passed.

A possible solution will use this method instead.

//code edited from here

Edit:checked my template, It seems ,It does not work. Instead use

bp_core_fetch_avatar( array( 'item_id' =>YOURGROUPID, 'object' => 'group', 'type' => 'thumb', 'width' => 64 ,'height' => 64 ) )

Hope It helps.