Introduction
Creation of Automorphism Groups AutomorphismGroup(G): Grp -> GrpAuto Example GrpAuto_autogp-full (H58E1) AutomorphismGroup(G, Q, I): Grp, SeqEnum[GrpElt], SeqEnum[SeqEnum[GrpElt]] -> GrpAuto
Access Functions Group(A) : GrpAuto -> Grp NumberOfGenerators(A) : GrpAuto -> RngIntElt Generators(A) : GrpAuto -> SetEnum InnerGenerators(A) : GrpAuto -> SeqEnum CharacteristicSeries(A) : GrpAuto -> SeqEnum IsSoluble(A) : GrpAuto -> BoolElt
Order Functions Order(A) : GrpAuto -> RngIntElt FactoredOrder(A) : GrpAuto -> [ <RngIntElt, RngIntElt> ] OuterOrder(A) : GrpAuto -> RngIntElt Example GrpAuto_autogp-order (H58E2)
Representations of an Automorphism Group PermutationRepresentation(A) : GrpAuto -> Map, GrpPerm, SetIndx PermutationGroup(A) : GrpAuto -> GrpPerm PermutationSupport(A) : GrpAuto -> SetIndx FPGroup(A) : GrpAuto -> GrpFP, Map OuterFPGroup(A) : GrpAuto -> GrpFP, Map Example GrpAuto_autogp-rep1 (H58E3) Example GrpAuto_autogp-rep2 (H58E4)
Automorphisms A . i : GrpAuto, RngIntElt -> GrpAutoElt Identity(A) : GrpAuto -> GrpAutoElt A ! f : GrpAuto, Map -> GrpAutoElt Order(f) : GrpAutoElt -> RngIntElt f * g : GrpAutoElt, GrpAutoElt -> GrpAutoElt f ^ n : GrpAutoElt, RngIntElt -> GrpAutoElt (g1, ..., gr) : GrpAutoElt, ..., GrpAutoElt -> GrpAutoElt g eq h : GrpAutoElt, GrpAutoElt -> BoolElt g ne h : GrpAutoElt, GrpAutoElt -> BoolElt IsInner(f) : GrpAutoElt -> BoolElt, GrpElt Example GrpAuto_autogp-elts (H58E5) Example GrpAuto_characteristic-subgroups (H58E6)
Stored Attributes of an Automorphism Group HasAttribute(A, s) : GrpAuto, MonStgElt -> BoolElt, . Example GrpAuto_characteristicsubgps (H58E7) Example GrpAuto_auto-maximals (H58E8)
Holomorphs Holomorph(G) : Grp -> GrpPerm, HomGrp, HomGrp Holomorph(G, A) : Grp, GrpAuto -> GrpPerm, HomGrp, HomGrp
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