Frequency analysis of Vigenere Cipher
You should not just "pick the highest frequency character and assume it should be E" because it will probably fail most of the time, except if your ciphertext is really long.

If your alphabet is small enough (usually either 26 or 255), it would be wiser to try all the possibilities for each group, and to check if the output looks like real english (printable chars, correct frequency, etc). It will be almost as fast, and you'll be way more confident in your result.