As an additional feature of this package we provide some functions to
count extensions of *p*-groups and Lie algebras over *GF*(*p*). These
functions have been used in counting the 2-groups of size 2^{10}.

`NumberOfPClass2PGroups( n, p, k )`

determines the number of *n*-generator *p*-groups of *p*-class 2 with
Frattini subgroup of order 2^{k}.

`NumberOfPClass2PGroups( n, p )`

returns a list of of numbers of *n*-generator *p*-groups of *p*-class 2
with Frattini subgroup of order 2^{k} for *k* in 1, …, *n*(*n*+1)/2.

`NumberOfClass2LieAlgebras( n, p, k )`

determines the number of *n*-generator Lie algebras of class 2 over
*GF*(*p*) with derived Lie subalgebra of dimension *k*.

`NumberOfClass2LieAlgbras( n, p )`

returns a list of of numbers of *n*-generator Lie algebras of class 2
over *GF*(*p*) with derived Lie subalgebra of dimension *k* for *k* in
1, …, *n*(*n*−1)/2.

AutPGrp manual

July 2018