WITH d AS (
    SELECT dt.*,COUNT(DISTINCT id) OVER(PARTITION BY grp_id,c) cnt_c
      FROM (SELECT dt.*,SUBSTR(in_str,rn,1) c,rn
              FROM (SELECT data.*,COUNT(*) OVER (PARTITION BY grp_id) cnt FROM data) dt
                  ,(SELECT ROWNUM rn FROM (SELECT MAX(LENGTH(in_str)) len FROM data) CONNECT BY ROWNUM<=len)
             WHERE rn<=LENGTH(in_str)
            ) dt
)
,t(id,grp_id,in_str,rn,w,cnt) AS (
    SELECT id,grp_id,in_str,rn,c,cnt FROM d
    UNION ALL
    SELECT d.id,d.grp_id,d.in_str,d.rn,t.w||d.c,t.cnt
      FROM t,d
     WHERE t.id = d.id AND t.rn<d.rn
)
SELECT grp_id,w
  FROM (SELECT grp_id,w,rank() OVER(PARTITION BY grp_id ORDER BY LENGTH(w) DESC) rnk
         FROM t
         GROUP BY grp_id,w
         HAVING COUNT(DISTINCT id) = MAX(cnt)
        )
WHERE rnk=1
;

    GRP_ID W
---------- ------------
        10 ARACDA
        10 BRACDA
        20 HHTHTHT
        20 THHTHHT
        30 PRAI
        40 HMAN
        50 TENone