In this talk, I will present quantum query complexity of symmetric oracle problems. In particular, we will be exploring the query complexity of quantum learning problems in which the oracles form a group G of unitary matrices, and a description of the optimal success probability of a t-query quantum algorithm in terms of group characters. More generally, in the coset identification problem, for a subgroup H of group G, the task is to determine which coset the group element belongs to. The authors provide character-theoretic formulas for the optimal success probability achieved by a t-query algorithm for this problem. It generalizes a number of well-known quantum algorithms including the Bernstein-Vazirani problem, the van Dam problem and finite field polynomial interpolation.