How to save data of an input field to an array

Don’t use update_usermeta, it is deprecated, update_user_meta is the one to use.

You get the previously saved value out with get_user_meta.

<input type="text" name="group[]" id='group[]' class="regular-text"
    value="<?php echo esc_attr( get_user_meta( $user->ID, 'group', true ) ); ?>" />