1%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2%% 3%A additional.tex AutPGrp documentation Bettina Eick 4%A Eamonn O'Brien 5%% 6 7%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 8\Chapter{Additional Features of the Package} 9 10As an additional feature of this package we provide some functions to 11count extensions of $p$-groups and Lie algebras over $GF(p)$. These 12functions have been used in counting the $2$-groups of size $2^{10}$. 13 14\> NumberOfPClass2PGroups( n, p, k ) 15 16determines the number of $n$-generator $p$-groups of $p$-class 2 with 17Frattini subgroup of order $2^k$. 18 19\> NumberOfPClass2PGroups( n, p ) 20 21returns a list of of numbers of $n$-generator $p$-groups of $p$-class 2 22with Frattini subgroup of order $2^k$ for $k$ in $1, \ldots, n(n+1)/2$. 23 24\> NumberOfClass2LieAlgebras( n, p, k ) 25 26determines the number of $n$-generator Lie algebras of class 2 over 27$GF(p)$ with derived Lie subalgebra of dimension $k$. 28 29\> NumberOfClass2LieAlgbras( n, p ) 30 31returns a list of of numbers of $n$-generator Lie algebras of class 2 32over $GF(p)$ with derived Lie subalgebra of dimension $k$ for $k$ in 33$1, \ldots, n(n-1)/2$. 34 35%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 36