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asocgen: Overview

asocgen is a small, personal project that I use to explore finite groups and programming in plain old C. In this project groups are (mostly) treated as black-box objects, defined only by their multiplication table. The asocgen library is setup to handle groups of order up to 65534 (that is 0xfffe; thus elements fitting into a 2-byte word).

The main features of asocgen include:

  • Construction of well-known families of groups such as the symmetric groups or cyclic groups.
  • Discovery and analysis of subgroups of larger groups such as S7.
  • Computing information about groups (treated as black-box-objects) such as order, whether a groups is commutative or simple or computing (minimal) generating sets.
  • Testing for isomorphism using an algorithm that uses minimal generating sets. This slightly improves on naive approach but the runtime is still infeasable for groups of higher order.
  • Storing and reading groups via .txt files containing the full group multiplication table.


All code is written in plain C using a subset of the C99 features. For compilation it is recommended to use the gcc compiler on a UNIX system. In addition to stdlib the following external dependencies are required:

  • elfclib, a small C library containing generic utility and data structures.
  • dirent.h, POSIX header to read directory contents.

To compile asocgen do the following:

  • Adapt the paths in lines 2 and 3 of the MAKEFILE to include and link elfclib.
  • Call sh or alternatively call make with the appropriate command-line arguments manually.

Application and Run

In the current state of the project there exists no general asocgen application. Instead main.c is used to program whatever application of the asocgen library is needed. By compiling, an executable bin/asoc is then produced executing this code.

This may change in the (near) future and asocgen may come with an executable and perhaps an interactive interface to provide easier access to the library functions.