# Access Functions

The functions described here provide access to basic information stored for an automorphism group $A$.

## `Group(A): GrpAuto -> Grp`

Given a group of automorphisms $A$ of the group $G$, return the base group $G$ on which $A$ acts.

## `NumberOfGenerators(A): GrpAuto -> RngIntElt`

## `Ngens(A): GrpAuto -> RngIntElt`

Given a group of automorphisms $A$ of the group $G$, return the number of defining generators for $A$.

## `NumberOfPCGenerators(A): GrpAuto -> RngIntElt`

## `NPCGenerators(A): GrpAuto -> RngIntElt`

## `NPCgens(A): GrpAuto -> RngIntElt`

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 $A$.

## `Generators(A): GrpAuto -> SetEnum`

Given a group of automorphisms $A$ of the group $G$, return a set containing the defining generators of $A$.

## `PCGenerators(A): GrpAuto -> SetIndx`

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 $A$.

## `InnerGenerators(A): GrpAuto -> SeqEnum`

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.

## `CharacteristicSeries(A): GrpAuto -> SeqEnum`

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.

## `IsSoluble(A): GrpAuto -> BoolElt`

## `IsSolvable(A): GrpAuto -> BoolElt`

Given a group of automorphisms $A$ of the group $G$, return the value of $A$’s attribute `Soluble`, if this attribute has been set.

## `IsSolubleAutomorphismGroupPGroup(A): GrpAuto -> BoolElt`

## `IsSolvableAutomorphismGroupPGroup(A): GrpAuto -> BoolElt`

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 $A$.