How do I solve this Vigenere cipher. Unknown key

I have this cipher text:

hrmwnuurseae ucsmnktyqwnc gnheepquvwai uiggmvvofmrp eaikaipoxlog tamkeykmxzev xiplhrvmifdf nizwsrhtijty gmxzexqohasf htmftvtrivwz vhxzeztbsfej uopwtzvbioik jcewsrttlwnf dlitrlvuwzak jtsddpqugsej crassrobmlif wsmxikyevwsf ktassrirmwvf wsjsucvarvgi kezgujnylsty eaikaicnwoei gdmlhvteyfdv tlisvvqffjuk wsefdkjevwsk hovtrlvuwasr phsfoltafded cnwgaigtlwyr nledlyqnsmrr dlieeeeoqwij reecieeaikai ufyfeicl

(The key is "ceasar", but I have to know how to solve it without knowing the key.)

Step 1

I have been able to find the key length of 6. Next what I did was take every sixth letter from the cipher text(modulo 6):

huutgquveptkxvnhgqhtvtuvjtdvjqcowykiwvknecgttqwjhvptcgnqdereu

All these letter should have been encoded with the same letter from the key, so it's a simple shift cipher.

I made a frequency analysis on it.

So I came to the conclusion that T is probably E

Step 2

Shift the text so T becomes E

Plaintext:

sfferbfgpaevigysrbsegefgueogubnzhjvthgvypnreebhusgaenrybopcpf

Let's see if this matches the known key by trying to encode S.

So if I'm getting this right, which I don't, I should look at the Vigenere square. Look at which letter in the key would convert S to H. In this case it would be P, but that would say that the first letter of the key is P which it isn't.

Can you see what I'm doing wrong?

* This article was originally published here