Stabilizers for GF(5)-representable matroids

The matroid terminology follows Oxley [4]. Two r×n matrices A and A′ representing the same matroid M over a field GF(q) are called projectively equivalent representations of M if one can be obtained from the other by elementary row operations and column scaling. Otherwise they are called projectively inequivalent. The matrices A and A′ are called equivalent representations of M if, in addition to elementary row operations and column scaling, A′ may be obtained from A by replacing each entry of A by its image under a non-trivial automorphism of GF(q). Otherwise they are called inequivalent representations. For prime fields, as in this case, projective equivalence and equivalence coincide as prime fields do not have non-trivial automorphisms.