Basic Group Properties
IsExtraSpecial(G) : GrpPC -> BoolElt
IsSpecial(G) : GrpPC -> BoolElt
pClass(G) : GrpPC -> RngIntElt
pRanks(G) : GrpPC-> [ RngIntElt ]
CharacterDegrees(G) : GrpFin -> [ Tup ]
CharacterDegreesPGroup(G) : GrpFin -> [ RngIntElt ]
CharacterTableConlon(G) : GrpPC -> [ AlgChtrElt ]
Subgroups and Subgroup Series
Agemo(G, i) : GrpPC, RngIntElt -> GrpPC
JenningsSeries(G) : GrpPC -> [GrpPC]
Omega(G, i) : GrpPC, RngIntElt -> GrpPC
Generating p-groups
GeneratepGroups (p, d, c : parameters) : RngIntElt, RngIntElt,RngIntElt -> [GrpPC], RngIntElt
Descendants(G : parameters) : GrpPC -> [GrpPC], RngIntElt
Example GrpPGp_Generating_p_groups (H23E1)
Example GrpPGp_GeneratepGroups (H23E2)
Example GrpPGp_IsGood (H23E3)
Isomorphism Testing and Standard Presentations
StandardPresentation(G): GrpPC -> GrpPC, Map
IsIdenticalPresentation(G, H) : GrpPC, GrpPC -> BoolElt
IsIsomorphic(G, H) : GrpPC, GrpPC -> BoolElt, Map
Example GrpPGp_StandardPresentation (H23E4)
Automorphism Group Algorithm
AutomorphismGroup(G): GrpPC -> GrpAuto
Example GrpPGp_AutomorphismGroup (H23E5)
Counting p-groups
ClassTwo(p, d : parameters) : RngIntElt, RngIntElt -> SeqEnum
Example GrpPGp_ClassTwo (H23E6)
The p-groups of Order Dividing p^7
SearchPGroups(p, n: parameters) : RngIntElt, RngIntElt -> SeqEnum
CountPGroups(p, n: parameters) : RngIntElt, RngIntElt -> SeqEnum
Example GrpPGp_p7 (H23E7)
Metacyclic p-groups
MetacyclicPGroups(p, n: parameters) : RngIntElt, RngIntElt -> SeqEnum
IsMetacyclicPGroup (P) : Grp -> BoolElt
InvariantsMetacyclicPGroup (P) : Grp -> Tup
StandardMetacyclicPGroup (P): Grp -> GrpPC
NumberOfMetacyclicPGroups (p, n): RngIntElt, RngIntElt -> SeqEnum
HasAllPQuotientsMetacyclic (G): GrpFP -> BoolElt, SeqEnum
Example GrpPGp_meta (H23E8)
Miscellanous p-group functions
NumberOfSubgroupsAbelianPGroup (A) : SeqEnum -> SeqEnum
OrderAutomorphismGroupAbelianPGroup (A) : SeqEnum -> RngIntElt