Get group avatar

  $GroupAvatarUrl = bp_core_fetch_avatar([
    'item_id' => $GroupId,
    'object'  => 'group',
    'type'    => 'full',    //'thum' or 'full'
    'html'    => false
  ]);
  if ($GroupAvatarUrl)   //Optional - Append a changing query string to the image URL (to force it to be reloaded if browser has cached)
    $GroupAvatarUrl = add_query_arg( 'v', time(), $GroupAvatarUrl );
  $GroupAvatarUrl = esc_url($GroupAvatarUrl);

Replace the default group avatar

//*****************************************************
//*****************************************************
//********** CHANGE THE DEFAULT GROUP AVATAR **********
//*****************************************************
//*****************************************************
add_filter( 'bp_get_group_avatar', 'my_default_get_group_avatar');
function my_default_get_group_avatar($avatar)
{
  global $bp, $groups_template;

  if( strpos($avatar,'group-avatars') || (!is_object($groups_template)))
  {
    return $avatar;
  }
  else
  {
    $custom_avatar = get_stylesheet_directory_uri() . '/images/my_image_name.png';

    if($bp->current_action == "")
      return '<img class="avatar" src="'.$custom_avatar.'" alt="' . esc_attr( $groups_template->group->name ) . '" width="'.BP_AVATAR_THUMB_WIDTH.'" height="'.BP_AVATAR_THUMB_HEIGHT.'" />';
    else
      return '<img class="avatar" src="'.$custom_avatar.'" alt="' . esc_attr( $groups_template->group->name ) . '" width="'.BP_AVATAR_FULL_WIDTH.'" height="'.BP_AVATAR_FULL_HEIGHT.'" />';
  }
}

add_filter('bp_core_default_avatar_group', 'MyGroupDefaultAvatar', 10, 2);
function MyGroupDefaultAvatar($Avatar, $Params)
{
  $custom_avatar = get_stylesheet_directory_uri() .'/images/my_image_name.png';
  return ($custom_avatar);
}