Ancient greek for twenty-six is "eikosi (kai) hex" or "hex (kai) eikosi(n)". 26 is κϝ′ (or κϛ′). (Smyth 347 D) I guess that might make the English word "hexecosinal" or some such (I don't think there is any Greek-derived word for base 26 in English).

However, since "decimal" and cousins come from Latin, you would want a word like "sevigesimal" ("vigesimal" is the adjective for base 20 and "sedecimal", not "hexadecimal" is the fully latinate adjective for base 16). But, as I said before, this is not a base-N numeral system, so it shouldn't be called "sevigesimal".

Update: Here is an interesting link. Also, interestingly, as with "hexadecimal"/"sedecimal", apparently there is a mixed Greek-Latin form for base 17, "heptadecimal" in addition to the latinate "septendecimal".

Update 2: changed "κς′" to "κϝ′ (or κϛ′)". The sigma+tau symbol in my printed copy of Smyth looked like a final sigma, so I assumed that and didn't actually think about it being wrong for sigma to come between epsilon and zeta. I was further confused by the use of a normal sigma in the chart on the online version of Smyth. This all struck me at some point when I recalled learning in school that the symbol is actually "digamma", so I've since sorted things out and amended this post.