#############################################################################
##
#A anupqeg.tst ANUPQ package Greg Gamble
##
## Tests all but one of the ANUPQ examples.
## Execute this file with `Test( "anupqeg.tst" );'.
## This is a *big* test, taking some 40 minutes on a *fast* (1GHz) machine.
## The number of GAPstones returned at the end do not mean much as they do
## not measure the time spent by the `pq' binary.
##
gap> START_TEST( "Testing ANUPQ examples" );
gap> SetInfoLevel(InfoANUPQ, 1);
gap> examples := AllPqExamples();
[ "11gp-3-Engel-Id", "11gp-3-Engel-Id-i", "11gp-PG-i", "11gp-Rel-i",
"11gp-SP-a-Rel-1-i", "11gp-SP-a-Rel-i", "11gp-SP-a-i", "11gp-SP-b-Rel-i",
"11gp-SP-b-i", "11gp-SP-c-Rel-i", "11gp-a-Rel-i", "11gp-i", "2gp-PG-2-i",
"2gp-PG-3-i", "2gp-PG-4-i", "2gp-PG-e4-i", "2gp-PG-i", "2gp-Rel",
"2gp-Rel-i", "2gp-SP-1-Rel-i", "2gp-SP-2-Rel-i", "2gp-SP-3-Rel-i",
"2gp-SP-4-Rel-i", "2gp-SP-Rel-i", "2gp-SP-d-Rel-i", "2gp-a-Rel-i",
"3gp-PG-4-i", "3gp-PG-i", "3gp-PG-x-1-i", "3gp-PG-x-i", "3gp-Rel-i",
"3gp-SP-1-Rel-i", "3gp-SP-2-Rel-i", "3gp-SP-3-Rel-i", "3gp-SP-4-Rel-i",
"3gp-SP-Rel-i", "3gp-a-Rel", "3gp-a-Rel-i", "3gp-a-x-Rel-i",
"3gp-maxoccur-Rel-i", "5gp-PG-i", "5gp-Rel-i", "5gp-SP-Rel-i",
"5gp-SP-a-Rel-i", "5gp-SP-b-Rel-i", "5gp-SP-big-Rel-i", "5gp-SP-d-Rel-i",
"5gp-a-Rel-i", "5gp-b-Rel-i", "5gp-c-Rel-i", "5gp-maxoccur-Rel-i",
"5gp-metabelian-Rel", "5gp-metabelian-Rel-i", "7gp-PG-i", "7gp-Rel-i",
"7gp-SP-Rel-i", "7gp-SP-a-Rel-i", "7gp-SP-b-Rel-i", "B2-4", "B2-4-Id",
"B2-4-SP-i", "B2-5", "B2-5-i", "B2-8-i", "B4-4-a-i", "B4-4-i", "B5-4.g",
"B5-5-Engel3-Id", "EpimorphismStandardPresentation",
"EpimorphismStandardPresentation-i", "F2-5-i", "G2-SP-Rel-i",
"G3-SP-Rel-i", "G5-SP-Rel-i", "G5-SP-a-Rel-i", "IsIsomorphicPGroup-ni",
"Nott-APG-Rel-i", "Nott-PG-Rel-i", "Nott-SP-Rel-i", "Pq", "Pq-ni",
"PqDescendants-1", "PqDescendants-1-i", "PqDescendants-2",
"PqDescendants-3", "PqDescendants-treetraverse-i",
"PqDescendantsTreeCoclassOne-16-i", "PqDescendantsTreeCoclassOne-25-i",
"PqDescendantsTreeCoclassOne-9-i", "PqEpimorphism", "PqPCover",
"PqSupplementInnerAutomorphisms", "R2-5-i", "R2-5-x-i",
"StandardPresentation", "StandardPresentation-i", "gp-256-SP-Rel-i" ]
gap> RemoveSet(examples, "EpimorphismStandardPresentation-i");
gap> nexamples := Length( examples );
96
gap> ##Example: "11gp-3-Engel-Id" . . . 3-Engel group for prime 11
gap> ##Non-trivial example of using the `Identities' option
gap> F := FreeGroup("a", "b"); a := F.1; b := F.2;
<free group on the generators [ a, b ]>
a
b
gap> G := F/[ a^11, b^11 ];
<fp group on the generators [ a, b ]>
gap> # All word pairs u, v in the pc generators of the 11-quotient Q of G
gap> # must satisfy the Engel identity: [u, v, v, v] = 1.
gap> f := function(u, v) return PqLeftNormComm( [u, v, v, v] ); end;
function( u, v ) ... end
gap> Q := Pq( G : Prime := 11, Identities := [ f ] );
#I Class 1 with 2 generators.
#I Class 2 with 3 generators.
#I Class 3 with 5 generators.
#I Class 3 with 5 generators.
<pc group of size 161051 with 5 generators>
gap> # We do a ``sample'' check that pairs of elements of Q do satisfy
gap> # the given identity:
gap> f( Random(Q), Random(Q) );
<identity> of ...
gap> f( Q.1, Q.2 );
<identity> of ...
gap> # Executing interactive variant of example: "11gp-3-Engel-Id"
gap> ##Example: "11gp-3-Engel-Id" . . . 3-Engel group for prime 11
gap> ##Non-trivial example of using the `Identities' option
gap> F := FreeGroup("a", "b"); a := F.1; b := F.2;
<free group on the generators [ a, b ]>
a
b
gap> G := F/[ a^11, b^11 ];
<fp group on the generators [ a, b ]>
gap> # All word pairs u, v in the pc generators of the 11-quotient Q of G
gap> # must satisfy the Engel identity: [u, v, v, v] = 1.
gap> f := function(u, v) return PqLeftNormComm( [u, v, v, v] ); end;
function( u, v ) ... end
gap> procId := PqStart( G );
1
gap> Q := Pq( procId : Prime := 11, Identities := [ f ] );
#I Class 1 with 2 generators.
#I Class 2 with 3 generators.
#I Class 3 with 5 generators.
#I Class 3 with 5 generators.
<pc group of size 161051 with 5 generators>
gap> # We do a ``sample'' check that pairs of elements of Q do satisfy
gap> # the given identity:
gap> f( Random(Q), Random(Q) );
<identity> of ...
gap> f( Q.1, Q.2 );
<identity> of ...
gap> ##Example: "11gp-3-Engel-Id-i" . . . 3-Engel grp for prime 11
gap> ##Variation of "11gp-3-Engel-Id" broken down into its lower-level component
gap> ##command parts.
gap> F := FreeGroup("a", "b"); a := F.1; b := F.2;
<free group on the generators [ a, b ]>
a
b
gap> G := F/[ a^11, b^11 ];
<fp group on the generators [ a, b ]>
gap> # All word pairs u, v in the pc generators of the 11-quotient Q of G
gap> # must satisfy the Engel identity: [u, v, v, v] = 1.
gap> f := function(u, v) return PqLeftNormComm( [u, v, v, v] ); end;
function( u, v ) ... end
gap> procId := PqStart( G : Prime := 11 );
2
gap> PqPcPresentation( procId : ClassBound := 1);
gap> PqEvaluateIdentities( procId : Identities := [f] );
#I Class 1 with 2 generators.
gap> for c in [2 .. 4] do
> PqNextClass( procId : Identities := [] ); #reset `Identities' option
> PqEvaluateIdentities( procId : Identities := [f] );
> od;
#I Class 2 with 3 generators.
#I Class 3 with 5 generators.
#I Class 3 with 5 generators.
gap> Q := PqCurrentGroup( procId );
<pc group of size 161051 with 5 generators>
gap> # We do a ``sample'' check that pairs of elements of Q do satisfy
gap> # the given identity:
gap> f( Random(Q), Random(Q) );
<identity> of ...
gap> f( Q.1, Q.2 );
<identity> of ...
gap> ##Example: "11gp-PG-i" . . . based on: examples/pga_11gp
gap> ##Descendants of C11 x C11 x C11
gap> F := FreeGroup("a", "b", "c");
<free group on the generators [ a, b, c ]>
gap> procId := PqStart(F : Prime := 11);
3
gap> PqPcPresentation(procId : ClassBound := 1,
> OutputLevel := 1);
#I Lower exponent-11 central series for [grp]
#I Group: [grp] to lower exponent-11 central class 1 has order 11^3
gap> PqComputePCover(procId);
#I Group: [grp] to lower exponent-11 central class 2 has order 11^9
gap> PqPGSupplyAutomorphisms(procId, [ [[ 2, 0, 0],
> [ 0, 1, 0],
> [ 0, 0, 1]],
>
> [[10, 0, 1],
> [10, 0, 0],
> [ 0,10, 0]] ]);
gap> PqPGConstructDescendants(procId : ClassBound := 2,
> CapableDescendants,
> StepSize := 1,
> RankInitialSegmentSubgroups := 3);
#I **************************************************
#I Starting group: [grp]
#I Order: 11^3
#I Nuclear rank: 6
#I 11-multiplicator rank: 6
#I # of immediate descendants of order 11^4 is 4
#I # of capable immediate descendants is 2
#I **************************************************
2
gap> PqQuitAll();
gap> ##Example: "11gp-Rel-i" . . . based on: examples/11gp
gap> ##(equivalent to "11gp-i" example but uses `Relators' option)
gap> F := FreeGroup("a", "b", "c");
<free group on the generators [ a, b, c ]>
gap> rels := ["[b, a, a, b, c]^11", "[a, b, b, a, b, c]^11", "(a * b)^11"];
[ "[b, a, a, b, c]^11", "[a, b, b, a, b, c]^11", "(a * b)^11" ]
gap> procId := PqStart(F : Prime := 11, Relators := rels);
1
gap> PqPcPresentation(procId : ClassBound := 7,
> OutputLevel := 1);
#I Lower exponent-11 central series for [grp]
#I Group: [grp] to lower exponent-11 central class 1 has order 11^3
#I Group: [grp] to lower exponent-11 central class 2 has order 11^8
#I Group: [grp] to lower exponent-11 central class 3 has order 11^19
#I Group: [grp] to lower exponent-11 central class 4 has order 11^42
#I Group: [grp] to lower exponent-11 central class 5 has order 11^98
#I Group: [grp] to lower exponent-11 central class 6 has order 11^228
#I Group: [grp] to lower exponent-11 central class 7 has order 11^563
gap> PqSavePcPresentation(procId, ANUPQData.outfile);
gap> ##Example: "11gp-SP-a-Rel-1-i" . . . based on: isom/11gp_a.com
gap> ##(like "11gp-SP-a-Rel-i" but the initial input presentation
gap> ## is only to class 1).
gap> F := FreeGroup("a", "b");
<free group on the generators [ a, b ]>
gap> rels := ["a^11", "b^11*[b, a, a]^-2", "[b, a, b, b, b, b]"];
[ "a^11", "b^11*[b, a, a]^-2", "[b, a, b, b, b, b]" ]
gap> procId := PqStart(F : Prime := 11, Relators := rels);
2
gap> PqSetOutputLevel(procId, 0);
gap> PqSPComputePcpAndPCover(procId : ClassBound := 1);
gap> PqSPStandardPresentation(procId, [ [[1,0],
> [0,1]],
>
> [[1,0],
> [0,1]],
>
> [[1,0],
> [0,1]],
>
> [[1,0],
> [3,1]],
>
> [[1,0],
> [9,3]],
>
> [[1,0],
> [6,6]],
>
> [[10,0],
> [2,1]] ]
>
> : # options
> ClassBound := 19,
> PcgsAutomorphisms);
gap> ##Example: "11gp-SP-a-Rel-i" . . . based on: isom/11gp_a.com
gap> ##(equivalent to "11gp-SP-a-i" but uses the `Relators' option)
gap> F := FreeGroup("a", "b");
<free group on the generators [ a, b ]>
gap> rels := ["a^11", "b^11*[b, a, a]^-2", "[b, a, b, b, b, b]"];
[ "a^11", "b^11*[b, a, a]^-2", "[b, a, b, b, b, b]" ]
gap> procId := PqStart(F : Prime := 11, Relators := rels);
3
gap> PqSetOutputLevel(procId, 0);
gap> PqSPComputePcpAndPCover(procId : ClassBound := 3);
gap> PqSPStandardPresentation(procId, [ [[1,0,0,0,1],
> [0,1,0,0,0]],
>
> [[1,0,0,0,0],
> [0,1,0,1,0]],
>
> [[1,0,0,0,0],
> [0,1,0,0,1]],
>
> [[1,0,0,0,0],
> [3,1,0,0,0]],
>
> [[1,0,0,0,0],
> [9,3,0,0,0]],
>
> [[1,0,0,0,0],
> [6,6,0,0,0]],
>
> [[10,0,0,0,0],
> [2,1,0,0,0]] ]
>
> : # options
> ClassBound := 19,
> PcgsAutomorphisms);
gap> PqQuitAll();
gap> ##Example: "11gp-SP-a-i" . . . based on: isom/11gp_a.com
gap> F := FreeGroup("a", "b"); a := F.1; b := F.2;
<free group on the generators [ a, b ]>
a
b
gap> R := [a^11, b^11/PqLeftNormComm([b, a, a])^2,
> PqLeftNormComm([b, a, b, b, b, b])];;
gap> procId := PqStart(F/R : Prime := 11);
1
gap> PqSetOutputLevel(procId, 0);
gap> PqSPComputePcpAndPCover(procId : ClassBound := 3);
gap> PqSPStandardPresentation(procId, [ [[1,0,0,0,1],
> [0,1,0,0,0]],
>
> [[1,0,0,0,0],
> [0,1,0,1,0]],
>
> [[1,0,0,0,0],
> [0,1,0,0,1]],
>
> [[1,0,0,0,0],
> [3,1,0,0,0]],
>
> [[1,0,0,0,0],
> [9,3,0,0,0]],
>
> [[1,0,0,0,0],
> [6,6,0,0,0]],
>
> [[10,0,0,0,0],
> [2,1,0,0,0]] ]
>
> : # options
> ClassBound := 19,
> PcgsAutomorphisms);
gap> ##Example: "11gp-SP-b-Rel-i" . . . based on: isom/11gp_b.com
gap> ##(equivalent to "11gp-SP-b-i" but uses the `Relators' option)
gap> F := FreeGroup("a", "b", "c");
<free group on the generators [ a, b, c ]>
gap> rels := ["a^11", "b^11", "c^11", "[b, a, a, a, b, a]",
> "[c, a]", "[c, b]", "[b, a, b]"];
[ "a^11", "b^11", "c^11", "[b, a, a, a, b, a]", "[c, a]", "[c, b]",
"[b, a, b]" ]
gap> procId := PqStart(F : Prime := 11, Relators := rels);
2
gap> PqSetOutputLevel(procId, 0);
gap> PqSPComputePcpAndPCover(procId : ClassBound := 3);
gap> PqSPStandardPresentation(procId, [ [[1,0,0,0,0],
> [0,1,0,0,1],
> [0,0,1,0,0]],
>
> [[1,0,0,0,0],
> [0,1,0,0,0],
> [0,0,1,0,1]],
>
> [[1,0,9,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[1,7,8,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[10,0,0,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[2,0,0,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[1,0,8,0,0],
> [0,1,3,0,0],
> [0,0,1,0,0]],
>
> [[1,0,9,0,0],
> [0,1,0,0,0],
> [0,0,3,0,0]],
>
> [[1,0,2,0,0],
> [0,1,0,0,0],
> [0,0,10,0,0]],
>
> [[1,9,10,0,0],
> [0,3,7,0,0],
> [0,0,6,0,0]],
>
> [[1,5,9,0,0],
> [0,7,4,0,0],
> [0,0,10,0,0]]]
>
> : # options
> ClassBound := 8,
> PcgsAutomorphisms);
gap> ##Example: "11gp-SP-b-i" . . . based on: isom/11gp_b.com
gap> F := FreeGroup("a", "b", "c"); a := F.1; b := F.2; c := F.3;
<free group on the generators [ a, b, c ]>
a
b
c
gap> R := [a^11, b^11, c^11, PqLeftNormComm([b, a, a, a, b, a]),
> Comm(c, a), Comm(c, b), PqLeftNormComm([b, a, b])];;
gap> procId := PqStart(F/R : Prime := 11);
3
gap> PqSetOutputLevel(procId, 0);
gap> PqSPComputePcpAndPCover(procId : ClassBound := 3);
gap> PqSPStandardPresentation(procId, [ [[1,0,0,0,0],
> [0,1,0,0,1],
> [0,0,1,0,0]],
>
> [[1,0,0,0,0],
> [0,1,0,0,0],
> [0,0,1,0,1]],
>
> [[1,0,9,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[1,7,8,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[10,0,0,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[2,0,0,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[1,0,8,0,0],
> [0,1,3,0,0],
> [0,0,1,0,0]],
>
> [[1,0,9,0,0],
> [0,1,0,0,0],
> [0,0,3,0,0]],
>
> [[1,0,2,0,0],
> [0,1,0,0,0],
> [0,0,10,0,0]],
>
> [[1,9,10,0,0],
> [0,3,7,0,0],
> [0,0,6,0,0]],
>
> [[1,5,9,0,0],
> [0,7,4,0,0],
> [0,0,10,0,0]]]
>
> : # options
> ClassBound := 8,
> PcgsAutomorphisms);
gap> PqQuitAll();
gap> ##Example: "11gp-SP-c-Rel-i" . . . based on: isom/11gp_c.com
gap> F := FreeGroup("a", "b", "c");
<free group on the generators [ a, b, c ]>
gap> rels := ["a^11", "b^11", "c^11", "[b, a, a, a, b]",
> "[c, a]", "[c, b]", "[b, a, b]"];
[ "a^11", "b^11", "c^11", "[b, a, a, a, b]", "[c, a]", "[c, b]", "[b, a, b]" ]
gap> procId := PqStart(F : Prime := 11, Relators := rels);
1
gap> PqSPComputePcpAndPCover(procId : ClassBound := 3);
gap> PqSPStandardPresentation(procId, [ [[1,0,0,0,0],
> [0,1,0,0,1],
> [0,0,1,0,0]],
>
> [[1,0,0,0,0],
> [0,1,0,0,0],
> [0,0,1,0,1]],
>
> [[1,0,9,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[1,7,8,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[10,0,0,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[2,0,0,0,0],
> [0,1,0,0,0],
> [0,0,1,0,0]],
>
> [[1,0,8,0,0],
> [0,1,3,0,0],
> [0,0,1,0,0]],
>
> [[1,0,9,0,0],
> [0,1,0,0,0],
> [0,0,3,0,0]],
>
> [[1,0,2,0,0],
> [0,1,0,0,0],
> [0,0,10,0,0]],
>
> [[1,9,10,0,0],
> [0,3,7,0,0],
> [0,0,6,0,0]],
>
> [[1,5,9,0,0],
> [0,7,4,0,0],
> [0,0,10,0,0]]]
>
> : # options
> ClassBound := 8,#for 9 perm.deg.>2^31, pq dies
> PcgsAutomorphisms);
gap> ##Example: "11gp-a-Rel-i" . . . based on: examples/11gpA
gap> F := FreeGroup("a", "b");
<free group on the generators [ a, b ]>
gap> rels := ["[b, a, a, b, b]^11", "[a, b, b, a, b, b]^11", "(a * b)^11"];
[ "[b, a, a, b, b]^11", "[a, b, b, a, b, b]^11", "(a * b)^11" ]
gap> procId := PqStart(F : Prime := 11, Relators := rels);
2
gap> PqPcPresentation(procId : ClassBound := 8,
> OutputLevel := 1);
#I Lower exponent-11 central series for [grp]
#I Group: [grp] to lower exponent-11 central class 1 has order 11^2
#I Group: [grp] to lower exponent-11 central class 2 has order 11^4
#I Group: [grp] to lower exponent-11 central class 3 has order 11^7
#I Group: [grp] to lower exponent-11 central class 4 has order 11^11
#I Group: [grp] to lower exponent-11 central class 5 has order 11^18
#I Group: [grp] to lower exponent-11 central class 6 has order 11^28
#I Group: [grp] to lower exponent-11 central class 7 has order 11^47
#I Group: [grp] to lower exponent-11 central class 8 has order 11^78
gap> PqSavePcPresentation(procId, ANUPQData.outfile);
gap> ##Example: "11gp-i" . . . based on: examples/11gp
gap> F := FreeGroup("a", "b", "c"); a := F.1; b := F.2; c := F.3;
<free group on the generators [ a, b, c ]>
a
b
c
gap> R := [PqLeftNormComm([b, a, a, b, c])^11,
> PqLeftNormComm([a, b, b, a, b, c])^11, (a * b)^11];;
gap> procId := PqStart(F/R : Prime := 11);
3
gap> PqPcPresentation(procId : ClassBound := 7,
> OutputLevel := 1);
#I Lower exponent-11 central series for [grp]
#I Group: [grp] to lower exponent-11 central class 1 has order 11^3
#I Group: [grp] to lower exponent-11 central class 2 has order 11^8
#I Group: [grp] to lower exponent-11 central class 3 has order 11^19
#I Group: [grp] to lower exponent-11 central class 4 has order 11^42
#I Group: [grp] to lower exponent-11 central class 5 has order 11^98
#I Group: [grp] to lower exponent-11 central class 6 has order 11^228
#I Group: [grp] to lower exponent-11 central class 7 has order 11^563
gap> PqSavePcPresentation(procId, ANUPQData.outfile);
gap> PqQuitAll();
gap> ##Example: "2gp-PG-2-i" . . . based on: examples/pga_example
gap> ##All class 3 descendants of C2 x C2 with extensive output
gap> F := FreeGroup("a", "b");
<free group on the generators [ a, b ]>
gap> procId := PqStart(F : Prime := 2);
1
gap> PqPcPresentation(procId : ClassBound := 1,
> OutputLevel := 1);
#I Lower exponent-2 central series for [grp]
#I Group: [grp] to lower exponent-2 central class 1 has order 2^2
gap> PqComputePCover(procId);
#I Group: [grp] to lower exponent-2 central class 2 has order 2^5
gap> PqPGSupplyAutomorphisms(procId, [ [[0,1],
> [1,1]],
>
> [[0,1],
> [1,0]] ]);
gap> PqPGConstructDescendants(procId : ClassBound := 3,
> PcgsAutomorphisms,
> CustomiseOutput := rec(group := [,,1],
> autgroup := [,1]));
#I **************************************************
#I Starting group: [grp]
#I Order: 2^2
#I Nuclear rank: 3
#I 2-multiplicator rank: 3
#I Group: [grp] #1;1 to lower exponent-2 central class 2 has order 2^3
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on 1^2 = 1 1
#I Non-trivial powers:
#I .1^2 = .3
#I Non-trivial commutators:
#I Automorphism 1:
#I Generator 1 --> 1 0 1
#I Generator 2 --> 0 1 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0
#I Generator 2 --> 0 1 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 1 1 0
#I Generator 2 --> 0 1 1
#I Group: [grp] #2;1 to lower exponent-2 central class 2 has order 2^3
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I Non-trivial powers:
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 0 1 0
#I Generator 2 --> 1 0 0
#I Group: [grp] #3;1 to lower exponent-2 central class 2 has order 2^3
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I Non-trivial powers:
#I .1^2 = .3
#I .2^2 = .3
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 0 1 0
#I Generator 2 --> 1 1 0
#I Automorphism 2:
#I Generator 1 --> 0 1 0
#I Generator 2 --> 1 0 0
#I # of immediate descendants of order 2^3 is 3
#I # of capable immediate descendants is 2
#I Group: [grp] #4;2 to lower exponent-2 central class 2 has order 2^4
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on 1^2 = 1 1
#I 4 is defined on 2^2 = 2 2
#I Non-trivial powers:
#I .1^2 = .3
#I .2^2 = .4
#I Non-trivial commutators:
#I Automorphism 1:
#I Generator 1 --> 1 0 1 0
#I Generator 2 --> 0 1 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 1
#I Generator 2 --> 0 1 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0
#I Generator 2 --> 0 1 1 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0
#I Generator 2 --> 0 1 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 0 1 0 0
#I Generator 2 --> 1 1 0 0
#I Automorphism 2:
#I Generator 1 --> 0 1 0 0
#I Generator 2 --> 1 0 0 0
#I Group: [grp] #5;2 to lower exponent-2 central class 2 has order 2^4
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1
#I Generator 2 --> 0 1 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0
#I Generator 2 --> 0 1 0 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 1 1 1 0
#I Generator 2 --> 0 1 1 1
#I Group: [grp] #6;2 to lower exponent-2 central class 2 has order 2^4
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .3
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1
#I Generator 2 --> 0 1 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0
#I Generator 2 --> 0 1 0 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 1 1 1 0
#I Generator 2 --> 0 1 1 1
#I # of immediate descendants of order 2^4 is 3
#I # of capable immediate descendants is 3
#I Group: [grp] #7;3 to lower exponent-2 central class 2 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I 5 is defined on 2^2 = 2 2
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 1
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 1 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 0 1 0 0 0
#I Generator 2 --> 1 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 0 1 0 0 0
#I Generator 2 --> 1 0 0 0 0
#I # of immediate descendants of order 2^5 is 1
#I # of capable immediate descendants is 1
#I **************************************************
#I **************************************************
#I Starting group: [grp] #1;1
#I Order: 2^3
#I Nuclear rank: 1
#I 2-multiplicator rank: 3
#I Group: [grp] #1;1 #1;1 to lower exponent-2 central class 3 has order 2^4
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on 1^2 = 1 1
#I Class 3
#I 4 is defined on 3^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .3
#I .3^2 = .4
#I Non-trivial commutators:
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1
#I Generator 2 --> 0 1 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0
#I Generator 2 --> 0 1 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 1 0
#I Generator 2 --> 0 1 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 0 0
#I Generator 2 --> 0 1 0 1
#I Group: [grp] #1;1 #2;1 to lower exponent-2 central class 3 has order 2^4
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on 1^2 = 1 1
#I Class 3
#I 4 is defined on 3^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .3
#I .3^2 = .4
#I Non-trivial commutators:
#I [ .2, .1 ] = .4
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1
#I Generator 2 --> 0 1 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0
#I Generator 2 --> 0 1 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 1 0
#I Generator 2 --> 0 1 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 0 0
#I Generator 2 --> 0 1 0 0
#I # of immediate descendants of order 2^4 is 2
#I # of capable immediate descendants is 1
#I **************************************************
#I Starting group: [grp] #2;1
#I Order: 2^3
#I Nuclear rank: 1
#I 2-multiplicator rank: 3
#I Group: [grp] #2;1 #1;1 to lower exponent-2 central class 3 has order 2^4
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I Class 3
#I 4 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .3^2 = .4
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .4
#I [ .3, .2 ] = .4
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0
#I Generator 2 --> 0 1 0 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 0 1 0 0
#I Generator 2 --> 1 0 0 0
#I Group: [grp] #2;1 #2;1 to lower exponent-2 central class 3 has order 2^4
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I Class 3
#I 4 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .3^2 = .4
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .4
#I [ .3, .2 ] = .4
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0
#I Generator 2 --> 0 1 0 1
#I Number of stabiliser generators is 0
#I Group: [grp] #2;1 #3;1 to lower exponent-2 central class 3 has order 2^4
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I Class 3
#I 4 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .4
#I .3^2 = .4
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .4
#I [ .3, .2 ] = .4
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0
#I Generator 2 --> 0 1 0 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 0 1 0 0
#I Generator 2 --> 1 0 0 0
#I # of immediate descendants of order 2^4 is 3
#I # of capable immediate descendants is 1
#I **************************************************
#I Starting group: [grp] #3;1
#I Order: 2^3
#I Nuclear rank: 0
#I 2-multiplicator rank: 1
#I Group [grp] #3;1 is an invalid starting group
#I **************************************************
#I Starting group: [grp] #4;2
#I Order: 2^4
#I Nuclear rank: 2
#I 2-multiplicator rank: 3
#I Group: [grp] #4;2 #1;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on 1^2 = 1 1
#I 4 is defined on 2^2 = 2 2
#I Class 3
#I 5 is defined on 3^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .3
#I .2^2 = .4
#I .3^2 = .5
#I Non-trivial commutators:
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 1
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 5
#I Automorphism 1:
#I Generator 1 --> 1 0 1 0 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 1 0 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 1 0
#I Automorphism 5:
#I Generator 1 --> 1 1 0 0 0
#I Generator 2 --> 0 1 1 0 0
#I Group: [grp] #4;2 #2;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on 1^2 = 1 1
#I 4 is defined on 2^2 = 2 2
#I Class 3
#I 5 is defined on 3^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .3
#I .2^2 = .4
#I .3^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 1
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 5
#I Automorphism 1:
#I Generator 1 --> 1 0 1 0 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 1 0 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 1 0
#I Automorphism 5:
#I Generator 1 --> 1 1 0 0 0
#I Generator 2 --> 0 1 1 0 0
#I # of immediate descendants of order 2^5 is 2
#I # of capable immediate descendants is 2
#I Group: [grp] #4;2 #3;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on 1^2 = 1 1
#I 4 is defined on 2^2 = 2 2
#I Class 3
#I 5 is defined on 3^2 = 1 1 1
#I 6 is defined on 4^2 = 2 2 2
#I Non-trivial powers:
#I .1^2 = .3
#I .2^2 = .4
#I .3^2 = .5
#I .4^2 = .6
#I Non-trivial commutators:
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 1 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 6
#I Automorphism 1:
#I Generator 1 --> 1 0 1 0 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 1 0 0 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 1 0 0
#I Automorphism 5:
#I Generator 1 --> 0 1 0 0 0 0
#I Generator 2 --> 1 1 0 0 0 0
#I Automorphism 6:
#I Generator 1 --> 0 1 0 0 0 0
#I Generator 2 --> 1 0 0 0 0 0
#I Group: [grp] #4;2 #4;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on 1^2 = 1 1
#I 4 is defined on 2^2 = 2 2
#I Class 3
#I 5 is defined on 3^2 = 1 1 1
#I 6 is defined on 4^2 = 2 2 2
#I Non-trivial powers:
#I .1^2 = .3
#I .2^2 = .4
#I .3^2 = .5
#I .4^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 1 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 5
#I Automorphism 1:
#I Generator 1 --> 1 0 1 0 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 1 0 0 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 1 0 0
#I Automorphism 5:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 1 1 0 0 0 0
#I # of immediate descendants of order 2^6 is 2
#I # of capable immediate descendants is 2
#I **************************************************
#I Starting group: [grp] #5;2
#I Order: 2^4
#I Nuclear rank: 3
#I 2-multiplicator rank: 4
#I Group: [grp] #5;2 #1;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .4^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 1
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0
#I Generator 2 --> 0 1 0 0 1
#I Group: [grp] #5;2 #2;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .4, .2 ] = .5
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0
#I Generator 2 --> 0 1 0 0 1
#I Group: [grp] #5;2 #3;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .4^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .4, .2 ] = .5
#I Number of stabiliser generators is 3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 1 0
#I Automorphism 3:
#I Generator 1 --> 1 1 1 0 0
#I Generator 2 --> 0 1 1 1 0
#I Group: [grp] #5;2 #4;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .4^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .4, .2 ] = .5
#I Number of stabiliser generators is 3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 1 0
#I Automorphism 3:
#I Generator 1 --> 1 1 1 0 0
#I Generator 2 --> 0 1 1 1 0
#I Group: [grp] #5;2 #5;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .3^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 1 0
#I Group: [grp] #5;2 #6;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .3^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 1 0
#I Group: [grp] #5;2 #7;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .3^2 = .5
#I .4^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I # of immediate descendants of order 2^5 is 7
#I # of capable immediate descendants is 3
#I Group: [grp] #5;2 #8;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .4^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .4, .2 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0 0
#I Generator 2 --> 0 1 0 0 1 1
#I Group: [grp] #5;2 #9;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .4^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .4, .2 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0 0
#I Generator 2 --> 0 1 0 0 1 1
#I Group: [grp] #5;2 #10;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .3^2 = .5
#I .4^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Group: [grp] #5;2 #11;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .3^2 = .5
#I .4^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Group: [grp] #5;2 #12;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on [3, 2] = 2 1 2
#I Non-trivial powers:
#I .1^2 = .4
#I .3^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .6
#I [ .4, .2 ] = .5 .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Group: [grp] #5;2 #13;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on [3, 2] = 2 1 2
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .3^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .6
#I [ .4, .2 ] = .5 .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Group: [grp] #5;2 #14;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on [3, 2] = 2 1 2
#I Non-trivial powers:
#I .1^2 = .4
#I .3^2 = .6
#I .4^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .6
#I [ .4, .2 ] = .5 .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Group: [grp] #5;2 #15;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on [3, 2] = 2 1 2
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .3^2 = .6
#I .4^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .6
#I [ .4, .2 ] = .5 .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0 0
#I Generator 2 --> 0 1 1 1 0 0
#I Group: [grp] #5;2 #16;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on [3, 2] = 2 1 2
#I Non-trivial powers:
#I .1^2 = .4
#I .3^2 = .6
#I .4^2 = .5 .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .6
#I [ .4, .2 ] = .5 .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 1 0 0
#I Automorphism 3:
#I Generator 1 --> 1 1 1 0 0 0
#I Generator 2 --> 0 1 1 1 0 0
#I Group: [grp] #5;2 #17;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on [3, 2] = 2 1 2
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .3^2 = .6
#I .4^2 = .5 .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .6
#I [ .4, .2 ] = .5 .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 1 0 0
#I Group: [grp] #5;2 #18;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on [3, 2] = 2 1 2
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .6
#I .3^2 = .6
#I .4^2 = .5 .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .6
#I [ .4, .2 ] = .5 .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 1 0 0
#I Automorphism 3:
#I Generator 1 --> 1 1 1 0 0 0
#I Generator 2 --> 0 1 1 1 0 0
#I # of immediate descendants of order 2^6 is 11
#I # of capable immediate descendants is 10
#I Group: [grp] #5;2 #19;3 to lower exponent-2 central class 3 has order 2^7
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on [3, 2] = 2 1 2
#I 7 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .3^2 = .6
#I .4^2 = .7
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .6
#I [ .4, .2 ] = .5 .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1 0
#I Generator 2 --> 0 1 0 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0 0
#I Generator 2 --> 0 1 0 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0 1
#I Group: [grp] #5;2 #20;3 to lower exponent-2 central class 3 has order 2^7
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on [3, 2] = 2 1 2
#I 7 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .3^2 = .6
#I .4^2 = .7
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .6
#I [ .4, .2 ] = .5 .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1 0
#I Generator 2 --> 0 1 0 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 0 1
#I Number of stabiliser generators is 1
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0 0
#I Generator 2 --> 0 1 0 0 0 0 0
#I Group: [grp] #5;2 #21;3 to lower exponent-2 central class 3 has order 2^7
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on [3, 2] = 2 1 2
#I 7 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .6
#I .3^2 = .6
#I .4^2 = .7
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I [ .3, .2 ] = .6
#I [ .4, .2 ] = .5 .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1 0
#I Generator 2 --> 0 1 0 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0 0
#I Generator 2 --> 0 1 0 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0 1
#I # of immediate descendants of order 2^7 is 3
#I # of capable immediate descendants is 3
#I **************************************************
#I Starting group: [grp] #6;2
#I Order: 2^4
#I Nuclear rank: 2
#I 2-multiplicator rank: 3
#I Group: [grp] #6;2 #1;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .3
#I .4^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 1
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0
#I Generator 2 --> 0 1 1 0 1
#I Group: [grp] #6;2 #2;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .3
#I .3^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 1 0
#I Automorphism 3:
#I Generator 1 --> 1 1 1 0 0
#I Generator 2 --> 0 1 1 1 0
#I Group: [grp] #6;2 #3;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .3 .5
#I .3^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 1 0
#I Automorphism 3:
#I Generator 1 --> 1 1 1 0 0
#I Generator 2 --> 0 1 1 1 0
#I Group: [grp] #6;2 #4;1 to lower exponent-2 central class 3 has order 2^5
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .3
#I .3^2 = .5
#I .4^2 = .5
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0
#I Generator 2 --> 0 1 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0
#I Generator 2 --> 0 1 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0
#I Generator 2 --> 0 1 1 0 0
#I # of immediate descendants of order 2^5 is 4
#I # of capable immediate descendants is 3
#I Group: [grp] #6;2 #5;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .3
#I .3^2 = .5
#I .4^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0 0
#I Generator 2 --> 0 1 1 0 1 1
#I Group: [grp] #6;2 #6;2 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I Class 3
#I 5 is defined on [3, 1] = 2 1 1
#I 6 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .3 .5
#I .3^2 = .5
#I .4^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 2
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 1 1 0 0 0
#I Generator 2 --> 0 1 1 0 1 1
#I # of immediate descendants of order 2^6 is 2
#I # of capable immediate descendants is 2
#I **************************************************
#I Starting group: [grp] #7;3
#I Order: 2^5
#I Nuclear rank: 5
#I 2-multiplicator rank: 5
#I Group: [grp] #7;3 #1;1 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I 5 is defined on 2^2 = 2 2
#I Class 3
#I 6 is defined on 4^2 = 1 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .4^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 1
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 1 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 1 0 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0
#I Automorphism 5:
#I Generator 1 --> 1 1 1 0 0 0
#I Generator 2 --> 0 1 1 1 0 0
#I Group: [grp] #7;3 #2;1 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I 5 is defined on 2^2 = 2 2
#I Class 3
#I 6 is defined on [4, 2] = 1 1 2
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .3^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .4, .2 ] = .6
#I [ .5, .1 ] = .6
#I Number of stabiliser generators is 5
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 1 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 1 0 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0
#I Automorphism 5:
#I Generator 1 --> 0 1 0 0 0 0
#I Generator 2 --> 1 0 0 0 0 0
#I Group: [grp] #7;3 #3;1 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I 5 is defined on 2^2 = 2 2
#I Class 3
#I 6 is defined on [4, 2] = 1 1 2
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .3^2 = .6
#I .4^2 = .6
#I .5^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .4, .2 ] = .6
#I [ .5, .1 ] = .6
#I Number of stabiliser generators is 6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 1 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 1 0 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0
#I Automorphism 5:
#I Generator 1 --> 0 1 0 0 0 0
#I Generator 2 --> 1 1 0 0 0 0
#I Automorphism 6:
#I Generator 1 --> 0 1 0 0 0 0
#I Generator 2 --> 1 0 0 0 0 0
#I Group: [grp] #7;3 #4;1 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
#I 2 is defined on image of defining generator 2
#I Class 2
#I 3 is defined on [2, 1] = 2 1
#I 4 is defined on 1^2 = 1 1
#I 5 is defined on 2^2 = 2 2
#I Class 3
#I 6 is defined on [3, 1] = 2 1 1
#I Non-trivial powers:
#I .1^2 = .4
#I .2^2 = .5
#I .3^2 = .6
#I Non-trivial commutators:
#I [ .2, .1 ] = .3
#I [ .3, .1 ] = .6
#I [ .5, .1 ] = .6
#I Automorphism 1:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 0 1
#I Number of stabiliser generators is 4
#I Automorphism 1:
#I Generator 1 --> 1 0 0 1 0 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 2:
#I Generator 1 --> 1 0 0 0 1 0
#I Generator 2 --> 0 1 0 0 0 0
#I Automorphism 3:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 1 0 0
#I Automorphism 4:
#I Generator 1 --> 1 0 0 0 0 0
#I Generator 2 --> 0 1 0 0 1 0
#I Group: [grp] #7;3 #5;1 to lower exponent-2 central class 3 has order 2^6
#I Class 1
#I 1 is defined on image of defining generator 1
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