The functions described here provide access to basic information stored for an automorphism group A.
Given a group of automorphisms A of the group G, return the base group G on which A acts.
Given a group of automorphisms A of the group G, return the number of defining generators for A.
Given a group of automorphisms A of the group G, where a pc-representation has been created for A (and attribute PCGenerators is set on A), return the number of pc-generators for A.
Given a group of automorphisms A of the group G, return a set containing the defining generators of A.
Given a group of automorphisms A of the group G, where a pc-representation has been created for A (and attribute PCGenerators is set on A), return an indexed set containing the pc-generators of A.
Given the full group of automorphisms A of the group G, return a sequence of generators for the inner automorphism group of the base group of A (attribute InnerGenerators), if this attribute has been set.
Given a group of automorphisms A of the group G, return the value of the characteristic series of G used to compute A, if this attribute has been set.
Given a group of automorphisms A of the group G, return the value of A's attribute Soluble, if this attribute has been set.
Given a group of automorphisms A of a p-group G constructed using the intrinsic AutomorphismGroup(G) or any equivalent alias, determine if A is soluble and return the result. This function also sets the Soluble attribute on A.