The following sections describe the solvable quotient functions (or sq
functions for short). SolvableQuotient allows to compute finite
solvable quotients of finitely presented groups.
The solvable quotient algorithm tries to find solvable quotients of a given finitely presented group G. First it computes the commutator factor group Q, which must be finite. It then chooses a prime p and repeats the following three steps: (1) compute all irreducible modules of Q over GF(p), (2) for each module M compute (up to equivalence) all extensions of Q by M, (3) for each extension E check whether E is isomorphic to a factor group of G. As soon as a non-trivial extension of Q is found which is still isomorphic to a factor group of G the process is repeated.
GAP 3.4.4