Tabular data synthesis is an emerging approach to circumvent strict regulations on data privacy while discovering knowledge through big data. Although state-of-the-art AI-based tabular data synthesizers, e.g., table-GAN, CTGAN, TVAE, and CTAB-GAN, are effective at generating synthetic tabular data, their training is sensitive to column permutations of input data. In this paper, we first c onduct a n e xtensive e mpirical s tudy to disclose such a property of permutation invariance and an in-depth analysis of the existing synthesizers. We show that changing the input column order worsens the statistical difference between real and synthetic data by up to 38.67% due to the encoding of tabular data and the network architectures. To fully unleash the potential of big synthetic tabular data, we propose two solutions: (i) AE-GAN, a synthesizer that uses an autoencoder network to represent the tabular data and GAN networks to synthesize the latent representation, and (ii) a feature sorting algorithm to find t he s uitable c olumn o rder o f i nput d ata f or CNN-based synthesizers. We evaluate the proposed solutions on five datasets in terms of the sensitivity to the column permutation, the quality of synthetic data, and the utility in downstream analyses. Our results show that we enhance the property of permutation-invariance when training synthesizers and further improve the quality and utility of synthetic data, up to 22%, compared to the existing synthesizers.@en