You could do something like this, based on the ascii values of the characters:
char[26] alphabet;
for(int i = 0; i <26; i++)
{
alphabet[i] = (char)(i+65); //65 is the offset for capital A in the ascaii table
}
(See the table here.) You are just casting from the int value of the character to the character value - but, that only works for ascii characters not different languages etc.
EDIT: As suggested by Mehrdad in the comment to a similar solution, it's better to do this:
alphabet[i] = (char)(i+(int)('A'));
This casts the A character to it's int value and then increments based on this, so it's not hardcoded.