I'm not sure what you mean by "derive".

For a more mathematical and geometric description of the super Poincaré group in general dimension you could check out

- Freed, [*Lectures on field theory and supersymmetry*][1] (Lecture 6);
- Freed, *Five lectures on supersymmetry*, AMS 1999 (Lecture 3);
- Deligne and Freed, [*Supersolutions* [arXiv:hep-th/9901094]][3] (Section 1.1), which can also be found in [*Quantum fields and strings: a course for mathematicians*][4];

plus the three additional references given for [super-Poincaré group at *nLab*][5]. 

For the 4d case see also

- Costello, e.g. [[arXiv:1401.2676]][2] (Section 1.1).

[1]: https://www.ma.utexas.edu/users/dafr/pcmi.pdf
[2]: https://arxiv.org/abs/1401.2676
[3]: http://arxiv.org/abs/hep-th/9901094
[4]: http://www.math.ias.edu/qft
[5]: https://ncatlab.org/nlab/show/super+Poincaré+group