Cranks are defined for partitions which combinatorially prove Ramanujan's congruences for the partition function modulo 5, 7, 11 and 25. Explicit bijections are given for the equinumerous crank classes. The key ingredients for proofs are two bijections for partitions and \(t\)-cores. These are used to find dihedral groups as symmetry groups of quadratic forms. Using \(q\)-series, some explicit formulas are given for the number of partitions which are \(t\)-cores. Related problems for self conjugate and distinct partitions are discussed.