Can we use CNN to effectively learn from a table whose various rows are permuted in the testing dataset, output for each remains same?

Question

I have a set of classes, 37 to be precise. Each class is represented by a feature vector of size [1,10]. A single input sample has the dimensions of [6,10], where each row in this sample represents a different class. Input only has one arrangement of these rows, whereas during testing, the rows can be permuted in the input sample and output should remain the same. Can I use CNN to drop the need of training on every permutation by using a kernel of size [1,10] which will effectively run slide vertically on the input sample? The size of the training dataset is considerably less(500 samples).