GAP (AutPGrp) - Chapter 5: Additional features of the package

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5 Additional features of the package
5.1 Additional features of the package
5.1-1 NumberOfPClass2PGroups
5.1-2 NumberOfPClass2PGroups
5.1-3 NumberOfClass2LieAlgebras
5.1-4 NumberOfClass2LieAlgbras

### 5 Additional features of the package

#### 5.1 Additional features of the package

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 \(2^{10}\).

##### 5.1-1 NumberOfPClass2PGroups

`‣ NumberOfPClass2PGroups`( n, p, k ) | ( operation )

This function determines the number of n-generator p-groups of p-class 2 with Frattini subgroup of order `2^k`.

##### 5.1-2 NumberOfPClass2PGroups

`‣ NumberOfPClass2PGroups`( n, p ) | ( operation )

This function 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 \(1, \ldots, n(n+1)/2\).

##### 5.1-3 NumberOfClass2LieAlgebras

`‣ NumberOfClass2LieAlgebras`( n, p, k ) | ( operation )

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

##### 5.1-4 NumberOfClass2LieAlgbras

`‣ NumberOfClass2LieAlgbras`( n, p ) | ( operation )

This function 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 \(1, \ldots, n(n-1)/2\).

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