CSI: Minecraft Items
Jelly, &nbsp;26&nbsp; 24 bytes

d64d1¦27Fża¥“csi”Fḟ0ȯ⁾0i


A full program taking the number and printing the result.
It does seem too long to me...

Try it online! or see the test suite.

How?

updating...

d64d1¦27Fża¥“csi”Fḟ0ȯ⁾0i - Main link: number n
 64                      - literal 64
d                        - divmod (whole divisions and remainder)
      27                 - literal 27
    1¦                   - apply to index 1 (the whole division from above)
   d                     - divmod
        F                - flatten into a single list (of three items i.e. [(n/64)/27, (n/64)%27, n%64]
            “csi”        - literal ['c','s','i']
           ¥             - last two links as a dyad:
         ż               -   zip
          a              -   logical and (any 0s in the divmod result become [0,0], others become [integer, character]
                 F       - flatten (from list of three lists to one list)
                  ḟ0     - filter discard zeros
                     ⁾0i - literal ['0','i']
                    ȯ    - logical or (non-vectorising)
                         - implicit print (smashed together representation, so [578703,'c',19,'i'] prints as 578703c19i)