Accurate characterization of glioma is crucial for clinical decision making. A delineation of the tumor is also desirable in the initial decision stages but is a time-consuming task. Leveraging the latest GPU capabilities, we developed a single multi-task convolutional neural network that uses the full 3D, structural, pre-operative MRI scans to can predict the IDH mutation status, the 1p/19q co-deletion status, and the grade of a tumor, while simultaneously segmenting the tumor. We trained our method using the largest, most diverse patient cohort to date containing 1508 glioma patients from 16 institutes. We tested our method on an independent dataset of 240 patients from 13 different institutes, and achieved an IDH-AUC of 0.90, 1p/19q-AUC of 0.85, grade-AUC of 0.81, and a mean whole tumor DICE score of 0.84. Thus, our method non-invasively predicts multiple, clinically relevant parameters and generalizes well to the broader clinical population.