Removing duplicate rows and appending from a table of lists

Question

For the table x with three lists per row:

x={{{10, 56, 528, 6240, 97920, 1751040, 38154240, 1058365440, 
    31677972480, 1134275788800, 45248407142400}, {2, 14, 15, 1, 
    2}, {1}}, {{3, 60, 280, 1232, 192192, 52276224, 17878468608, 
    74764505088, 1238954655744, 1152227829841920, 
    1534767469349437440}, {3, 6, 9, 3, 6}, {1}}, {{3, 60, 280, 1232, 
    192192, 52276224, 17878468608, 74764505088, 1238954655744, 
    1152227829841920, 1534767469349437440}, {3, 6, 10, 3, 6}, {1}}};

How can I convert the above table to this:

x2={{{10,56,528,6240,97920,1751040,38154240,1058365440,31677972480,1134275788800,45248407142400},{2,14,15,1,2},{1}},
{{3,60,280,1232,192192,52276224,17878468608,74764505088,1238954655744,1152227829841920,1534767469349437440},{3,6,10,3,6},{1},{3,6,9,3,6},{1}}};

Ie duplicates x[[n]][[1]] are removed and then for each duplicate n, x[[n]][[2]] and x[[n]][[3]] are appended to the row for the distinct n.

Also for x, how can the length be checked for how many lists are in x[[n]][[1]]? Is there a way to directly remove duplicate n's?

Thanks.

Answer 1

You can use GroupBy and KeyValueMap:

x3  = KeyValueMap[Join[{#}, ## & @@ Reverse@SortBy[First][#2]] &]@
    GroupBy[x, First -> Rest]

Also

x4 = KeyValueMap[Join[{#}, #2] &]@
  GroupBy[x, First -> Rest, Flatten[Reverse@SortBy[First]@#, 1] &]

x2 == x3 == x4

True

Answer 2

rule=Merge[Cases[
  Reverse@x, {w_,{y__},{z__}} :> w-> {{y},{z}}],Catenate]

And:

(Join[{#},#/.rule]&/@DeleteDuplicates[x[[All,1]]])==x2

True

If there is no good reason why {3, 6, 10, 3, 6}, should appear before {3, 6, 9, 3, 6} in the merged list (x2), change Reverse@x to x, but perhaps I am missing something important here?

Original Post

rule_alt=Catenate/@Merge[Cases[
  Reverse@x, {w_,{y__},{z__}} :> w-> {{y},{z}}],Join]