Conjugate(H, g) : GrpMat, GrpMatElt -> GrpMat

Construct the conjugate g^(-1) * H * g of the matrix group H by the matrix g. The group H and the element g must belong to a common matrix group.

Given groups H and K which belong to the same matrix group, construct the intersection of H and K.

CommutatorSubgroup(H, K) : GrpMat, GrpMat -> GrpMat

Given subgroups H and K of the group G, construct the commutator subgroup of H and K relative to G. If K is a subgroup of H, then G may be omitted.

Construct the centralizer of the matrix g in the group G; g and G must belong to a common matrix group.

Centralizer(G, H) : GrpMat, GrpMat -> GrpMat

Construct the centralizer of the group H in the group G; G and H must belong to a common matrix group.

Given a subgroup H of the matrix group G, construct the maximal normal subgroup of G that is contained in the subgroup H.

NormalClosure(G, H) : GrpMat, GrpMat -> GrpMat

Given a subgroup H of the matrix group G, construct the normal closure of H in G.

Given a subgroup H of the group G, construct the normalizer of H in G.

Given a group G and a prime p dividing the order of G, construct the maximal normal p-subgroup of G.

Sylow(G, p) : GrpMat, RngIntElt -> GrpMat

Given a group G and a prime p, construct the Sylow p-subgroup of G.