Glioma is a type of brain tumor, mostly diagnosed through biopsy or surgery. The prediction of glioma is still challenging to offer the required accurate solution for the diagnosis process. The challenge lies more at the edge of finding a solid feature representation rather than employing well-tuned classifiers. This paper proposes a solution to improve glioma prediction and diagnosis by proposing a rich combination of radiomic and genomic features. A novel feature extraction mechanism is proposed relying on the triple combination CNN-GLCM-DWT for MRI images and PCA for the genomics data. Several classical and deep learning classifiers are trained on the data. The proposed feature extraction is tested for validation on a dataset of 422 patients with low- or high-grade gliomas to predict three mutation statuses. Experiments prove the competency of the proposed mechanism when trained with an SVM classifier, which achieves high accuracy values of 97.5%, 96%, and 92% for the three mutations IDH1 mutation status, 1p/19q codeletion, and MGMT promotor methylation status, respectively. CNN as a deep learning method comes second with accuracy values of 95%,94.2%, and 88%, while the Random Forest comes last with values of87.5%, 80.7%, and 76%. Compared to existing related works that apply a single feature extraction method, the proposed triple combination CNN-GLCM-DWT feature extraction excels in classification accuracyfor the three mutation types by approximately 3.7%, 3.3%, and 10% inaccuracy. It is faster in average classification time by approximately 50%.