Basic Group Properties

This section lists predicates and structural properties which are only available for p-groups.

IsExtraSpecial(G) : GrpPC -> BoolElt

Given a p-group G, return true if G is extra-special, false otherwise.

IsSpecial(G) : GrpPC -> BoolElt

Given a p-group G, return true if G is special, false otherwise.

pClass(G) : GrpPC -> RngIntElt

The lower exponent-p class of the p-group G.

pRanks(G) : GrpPC-> [ RngIntElt ]

A sequence whose i-th entry is the number of pc-generators for the lower exponent-p class i quotient of the p-group G.

CharacterDegrees(G) : GrpFin -> [ RngIntElt ]

Given a finite p-group G, return the sequence [C_0, C_1, ... ], where C_i is the number of irreducible characters of G having degree p^i. For details of the algorithm see [Sla86].