Roughly speaking, the classical groups are groups of linear bijections of vector spaces over division rings, and subgroups singled out by requiring that some form (quadratic, bilinear, hermitian) be invariant. So each one of those groups is determined by some recipe, and some ingredients (a division ring, a number, a form, ...). E.g., a famous recipe named "A" takes a division ring K and a number n to produce the group SL(n,K), along with its relatives GL(n,K), PSL(n,K). Another recipe (no name given) takes a field R, a number n, and a non-degenerate quadratic form of Witt index i in n variables from R to produce the corresponding group of isometries.Conversely, the produced group determines the recipe and its ingredients, in general. However, there are some exceptions, including the reason why physicists study SL(2,C) while doing special relativity.The talk will report about such exceptions, and ways to understand deeper reasons for their occurrence.