The C standard, as I recall defines a byte effectively as at least 8 bits. I've read that some DSP platforms use a byte (and thus a char) that is 24 bits wide, because that's what audio samples use, but supposedly those platforms rarely, if ever, handle any actual text. The standard library contains a macro CHAR_BITS that tells you

I think I remember reading about a C compiler for the PDP-10 (or Lisp Machine?), also a 36-bit machine, that used a 9 bit byte. There even exists a semi-jocular RFC for UTF-9 and UTF-18.