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#
gap> START_TEST("integration.tst");
#
gap> testOrder:=function(n)
> local G, H, d, i;
> d := NrSmallGroups(n);
> for i in [1..d] do
> G:=SmallGroup(n, i);
> H:=PcGroupCode(CodePcGroup(G), n);
> Assert(0, not HasIdGroup(H));
> if IdGroup(H) <> [n,i] then
> Error("failure at ", [n,i]);
> fi;
> od;
> SmallGroupsInformation(n);
> end;;
#
gap> testOrder(13^3*2);
There are 15 groups of order 4394.
The groups of order p^3q are solvable by Burnside's pq-Theorem.
These groups are sorted by their Sylow subgroups.
1 - 3 are abelian.
4 - 5 are nonabelian nilpotent and have a normal Sylow 13-subgroup and a
normal Sylow 2-subgroup.
6 is non-nilpotent and has a normal Sylow 2-subgroup with Sylow
13-subgroup [ 2197, 1 ].
7 - 9 are non-nilpotent and have a normal Sylow 2-subgroup with Sylow
13-subgroup [ 2197, 2 ].
10 - 12 are non-nilpotent and have a normal Sylow 2-subgroup with Sylow
13-subgroup [ 2197, 5 ].
13 - 14 are non-nilpotent and have a normal Sylow 2-subgroup with Sylow
13-subgroup [ 2197, 3 ].
15 is non-nilpotent and has a normal Sylow 2-subgroup with Sylow
13-subgroup [ 2197, 4 ].
This size belongs to layer 12 of the SmallGroups library.
IdSmallGroup is available for this size.
gap> testOrder(13^3*3);
There are 19 groups of order 6591.
The groups of order p^3q are solvable by Burnside's pq-Theorem.
These groups are sorted by their Sylow subgroups.
1 - 3 are abelian.
4 - 5 are nonabelian nilpotent and have a normal Sylow 13-subgroup and a
normal Sylow 3-subgroup.
6 is non-nilpotent and has a normal Sylow 3-subgroup with Sylow
13-subgroup [ 2197, 1 ].
7 - 10 are non-nilpotent and have a normal Sylow 3-subgroup with Sylow
13-subgroup [ 2197, 2 ].
11 - 15 are non-nilpotent and have a normal Sylow 3-subgroup with Sylow
13-subgroup [ 2197, 5 ].
16 - 18 are non-nilpotent and have a normal Sylow 3-subgroup with Sylow
13-subgroup [ 2197, 3 ].
19 is non-nilpotent and has a normal Sylow 3-subgroup with Sylow
13-subgroup [ 2197, 4 ].
This size belongs to layer 12 of the SmallGroups library.
IdSmallGroup is available for this size.
gap> testOrder(13^3*5);
There are 5 groups of order 10985.
The groups of order p^3q are solvable by Burnside's pq-Theorem.
These groups are sorted by their Sylow subgroups.
1 - 3 are abelian.
4 - 5 are nonabelian nilpotent and have a normal Sylow 13-subgroup and a
normal Sylow 5-subgroup.
This size belongs to layer 12 of the SmallGroups library.
IdSmallGroup is available for this size.
gap> testOrder(13^3*7);
There are 7 groups of order 15379.
The groups of order p^3q are solvable by Burnside's pq-Theorem.
These groups are sorted by their Sylow subgroups.
1 - 3 are abelian.
4 - 5 are nonabelian nilpotent and have a normal Sylow 13-subgroup and a
normal Sylow 7-subgroup.
6 is non-nilpotent and has a normal Sylow 7-subgroup with Sylow
13-subgroup [ 2197, 5 ].
7 is non-nilpotent and has a normal Sylow 7-subgroup with Sylow
13-subgroup [ 2197, 3 ].
This size belongs to layer 12 of the SmallGroups library.
IdSmallGroup is available for this size.
gap> testOrder(13^3*11);
There are 5 groups of order 24167.
The groups of order p^3q are solvable by Burnside's pq-Theorem.
These groups are sorted by their Sylow subgroups.
1 - 3 are abelian.
4 - 5 are nonabelian nilpotent and have a normal Sylow 13-subgroup and a
normal Sylow 11-subgroup.
This size belongs to layer 12 of the SmallGroups library.
IdSmallGroup is available for this size.
gap> testOrder(37^3*7);
There are 6 groups of order 354571.
The groups of order p^3q are solvable by Burnside's pq-Theorem.
These groups are sorted by their Sylow subgroups.
1 - 3 are abelian.
4 - 5 are nonabelian nilpotent and have a normal Sylow 37-subgroup and a
normal Sylow 7-subgroup.
6 is non-nilpotent and has a normal Sylow 7-subgroup with Sylow
37-subgroup [ 50653, 5 ].
This size belongs to layer 12 of the SmallGroups library.
IdSmallGroup is available for this size.
#
gap> STOP_TEST("integration.tst", 1);
[ Dauer der Verarbeitung: 0.16 Sekunden
(vorverarbeitet)
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