The visual appearance of an object is not only dependent on the intrinsic class but also affected by extrinsic factors like illumination and view angle, leading to the difficulty in unsupervised deep discriminative learning. Fortunately, we could often obtain some extrinsic information that specifies/indicates the extrinsic factors along with the unlabelled visual data without human annotation effort. In this work we explore the extrinsic information in unsupervised deep discriminative learning. We propose a novel model named SurrogaTe class learning with Extrinsic INformation (STEIN). In our model we exploit the extrinsic information in two perspectives, the local surrogate class geometry and the global representation distribution, to deal with the inter-class visual similarity and the intra-class visual discrepancy caused by the extrinsic factor, respectively. We evaluate our model on two discriminative tasks, i.e. person re-identification (RE-ID) and pose-invariant face recognition (PIFR). We find that the extrinsic information (camera view label in RE-ID and pose label in PIFR) can significantly improve the discriminability of the unsupervisedly learned representation. We also report new state-of-the-art unsupervised performances on both tasks.