56 of them.
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A septillion has 24 zeros. A decillion has 33 zeros. A septendecillion has 54 zeros. I can't find your term in any of my reference works, so I guess it can have as many (or as few) zeros as you want.
after undecillion, there is :duodecillion 1, 39 zeros tredecillion 1, 42 zeros quattuordecillion 1, 45 zeros quindecillion 1, 48 zeros sexdecillion 1, 51 zeros septendecillion 1, 54 zeros octodecillion 1, 57 zeros novemdecillion 1, 60 zeros vigintillion 1, 63 zeros googol 1, 100 zeros centillion 1, 303 zeros googolplex 1, 10googol zeros source: http://en.wikipedia.org/wiki/Names_of_large_numbers
There are 100 zeros in googol
There are fourteen zeros in 100 million million.
A googolplexian is equal to 10^(10^100), which means it has a 1 followed by a googol (10^100) zeros. Therefore, a googolplexian has 10^100 zeros.