Convert rows, columns and values in data frame into 3 distinct columns in R

Question

I have the following

rows names for df (AA, AB, AC)

df$12(WT, WT, MUT)

df$34(WT, WT, MUT)

df$56(MUT, WT, WT)

     12   34  56
AA   WT   WT  MUT
AB   WT   WT  WT
AC   MUT  MUT WT

I would like to get the following df2

df2$GS(AA, AB, AC, AA, AB, AC, AA, AB, AC)

df2$SI(12, 12, 12, 34, 34, 34, 56, 56, 56)

df2$NT(WT, WT, MUT, WT, WT, MUT, MUT, WT, WT)

     GS   SI  NT
     AA   12  WT
     AB   12  WT
     AC   12  MUT
     AA   34  WT
     AB   34  WT
     AC   34  MUT
     AA   56  MUT
     AB   56  WT
     AC   56  WT

My current code so far is

setDT(df, keep.rownames = TRUE)[]

But after that I am a bit lost on the next set of code to generate df2. Any help would be greatly appreciated.