Added the missing perfect groups of order up to a million

doc/ref/grplib.xml

@@ -297,42 +297,34 @@ It returns <K>fail</K> if no such group exists in the library.
 <Heading>Finite Perfect Groups</Heading>
 
 <Index>perfect groups</Index>
-The &GAP; library of finite  perfect groups provides, up to isomorphism,
-a list of all perfect groups whose sizes are less than  <M>10^6</M>  excluding
-the following sizes:
-<P/>
-<List>
-<Item>
-      For <M>n = 61440</M>, 122880, 172032, 245760, 344064, 491520, 688128, or
-      983040,  the perfect groups  of size  <M>n</M>  have not completely been
-      determined yet.  The library  neither provides  the number of these
-      groups nor the groups themselves.
-</Item>
-<Item>
-      For  <M>n = 86016</M>,  368640,  or  737280,  the library  does not  yet
-      contain  the perfect groups  of size  <M>n</M>,  it  only provides their
-      numbers which are 52, 46, and 54, respectively.
-</Item>
-</List>
-<P/>
-Except for these eleven sizes, the list of altogether 1097 perfect groups
-in the  library is complete.  It relies  on results of  Derek&nbsp;F. Holt and
-Wilhelm Plesken which  are published in their  book    <Q>Perfect Groups</Q>
-<Cite Key="HP89"/>. Moreover,   they     have  supplied us    with    files with
-presentations of 488 of the groups. In terms of  these, the remaining 607
-nontrivial groups in the library can be described as 276 direct products,
-107  central   products, and 224  subdirect  products.  They are computed
-automatically by suitable &GAP; functions whenever they are needed.  Two
-additional groups omitted from the book <Q>Perfect Groups</Q> have also been
-included.
+The &GAP; library of finite  perfect groups provides, up to isomorphism, a
+list of all perfect groups whose sizes are less than  <M>10^6</M>. 
+The groups of most of these orders have been enumerated by
+Derek&nbsp;F. Holt and Wilhelm Plesken and
+published in their  book    <Q>Perfect Groups</Q> <Cite Key="HP89"/>.
+For orders <M>n = 86016</M>,  368640,  or  737280 this work only counted the
+groups (but did not explicitly list them), the groups of orders
+<M>n = 61440</M>, 122880, 172032, 245760, 344064, 491520,
+688128, or 983040 were omitted.
 <P/>
 We are grateful to Derek Holt and Wilhelm Plesken for making their groups
 available to the &GAP; community  by contributing their files. It should
 be noted that  their book contains a  lot of further information for many
 of the library groups.  So we would like  to recommend  it to any  &GAP;
 user who is interested in the groups.
+The library of these has been brought into &GAP; format by Volkmar Felsch.
+<P/>
+Several additional groups omitted from the book <Q>Perfect Groups</Q> have also
+been included. Two groups -- one of order 450000 with a factor group of
+type <M>A_6</M> and the one of order 962280 -- were found by Jack Schmidt in
+2005. Two groups of order 243000 and one each of orders 729000, 871200, 878460
+were found in 2020 by Alexander Hulpke.
+<P/>
+The perfect groups of size less than <M>10^6</M> which had not been
+classified in the work of Holt and Plesken have been enumerated by Alexander
+Hulpke. They are stored directly and provide less construction information
+in their names.
 <P/>
-The library has been brought into &GAP; format by Volkmar Felsch.
 <P/>
 As  all groups are stored  by presentations, a permutation representation
 is obtained by coset enumeration. Note that some of the library groups do
@@ -343,7 +335,6 @@ Computations in these groups may be rather time consuming.
 <#Include Label="PerfectGroup">
 <#Include Label="PerfectIdentification">
 <#Include Label="NumberPerfectGroups">
-<#Include Label="NumberPerfectLibraryGroups">
 <#Include Label="SizeNumbersPerfectGroups">
 <#Include Label="DisplayInformationPerfectGroups">
 
@@ -1168,4 +1159,3 @@ gap> LargestMovedPoint( P2 );
 <!-- %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -->
 <!-- %% -->
 <!-- %E -->
-

grp/perf.gd

@@ -97,7 +97,7 @@ DeclareAttribute("PerfectIdentification", IsGroup );
 ##  One can iterate over the perfect groups library with:
 ##  <Example><![CDATA[
 ##  gap> for n in SizesPerfectGroups() do
-##  >      for k in [1..NrPerfectLibraryGroups(n)] do
+##  >      for k in [1..NrPerfectGroups(n)] do
 ##  >        pg := PerfectGroup(n,k);
 ##  >      od;
 ##  >    od;
@@ -116,42 +116,31 @@ DeclareGlobalFunction("SizesPerfectGroups");
 ##  <#GAPDoc Label="NumberPerfectGroups">
 ##  <ManSection>
 ##  <Func Name="NumberPerfectGroups" Arg='size'/>
+##  <Func Name="NrPerfectGroups" Arg='size'/>
+##  <Func Name="NumberPerfectLibraryGroups" Arg='size'/>
+##  <Func Name="NrPerfectLibraryGroups" Arg='size'/>
 ##
 ##  <Description>
 ##  returns the number of non-isomorphic perfect groups of size <A>size</A> for
 ##  each positive integer  <A>size</A> up to <M>10^6</M> except for the eight  sizes
 ##  listed at the beginning  of  this section for  which the number is not
 ##  yet known. For these values as well as for any argument out of range it
 ##  returns <K>fail</K>.
+##  <A>NrPerfectGroups</A> is a synonym for <Ref Func="NumberPerfectGroups"/>.
+##  Moreover <A>NumberPerfectLibraryGroups</A> (and its synonym <A>NrPerfectLibraryGroups</A>)
+##  exist for historical reasons, and return 0 instead of fail for arguments
+##  outside the library scope.
 ##  </Description>
 ##  </ManSection>
 ##  <#/GAPDoc>
 ##
 DeclareGlobalFunction("NumberPerfectGroups");
 DeclareSynonym("NrPerfectGroups",NumberPerfectGroups);
-
-
-#############################################################################
-##
-#F  NumberPerfectLibraryGroups( <size> )  . . . . . . . . . . . . . . . . . .
-##
-##  <#GAPDoc Label="NumberPerfectLibraryGroups">
-##  <ManSection>
-##  <Func Name="NumberPerfectLibraryGroups" Arg='size'/>
-##
-##  <Description>
-##  returns the number of perfect groups of size <A>size</A> which are available
-##  in the  library of finite perfect groups. (The purpose  of the function
-##  is  to provide a simple way  to formulate a loop over all library groups
-##  of a given size.)
-##  </Description>
-##  </ManSection>
-##  <#/GAPDoc>
-##
 DeclareGlobalFunction("NumberPerfectLibraryGroups");
 DeclareSynonym("NrPerfectLibraryGroups",NumberPerfectLibraryGroups);
 
 
+
 #############################################################################
 ##
 #F  PerfectGroup( [<filt>, ]<size>[, <n>] )

grp/perf.grp

@@ -25,11 +25,16 @@ local p,pos;
   if pos=fail then
     return fail;
   fi;
-  if IsBound(PERFGRP[pos]) then
+  if IsBound(PERFGRP[pos]) and PERFGRP[pos]<>fail and PERFGRP[pos][1]<>fail then
     return pos;
   fi;
   # get the file number
-  p:=PositionSorted(PERFRec.covered,pos);
+  p:=Position(PERFRec.newlyAdded,sz);
+  if p=fail then
+    p:=PositionSorted(PERFRec.covered,pos);
+  else
+    p:=12+p;
+  fi;
   ReadGrp(Concatenation("perf",String(p),".grp"));
   return pos;
 end );
@@ -81,30 +86,14 @@ InstallGlobalFunction( NumberPerfectGroups, function ( size )
     fi;
 end );
 
+InstallGlobalFunction(NumberPerfectLibraryGroups,function(size)
+local a;
+  a:=NumberPerfectGroups(size);
+  if a=fail then return 0;
+  else return a;fi;
+end);
 
-#############################################################################
-##
-#F  NumberPerfectLibraryGroups( size )
-##
-##  `NumberPerfectLibraryGroups'  returns the number of nonisomorphic perfect
-##  groups of size `size' for 1 <= size <= 1 000 000 which are available in the
-##  perfect groups library.
-##
-InstallGlobalFunction( NumberPerfectLibraryGroups, function ( size )
-local sizenum;
-
-    if size=1 then
-      return 1;
-    elif IsOddInt(size) then return 0;fi;
-    # get the number and return it.
-    sizenum := PerfGrpLoad( size );
-    if sizenum = fail or size in PERFRec.notAvailable then
-        return 0;
-    else
-        return PERFRec.number[sizenum];
-    fi;
 
-end );
 
 #############################################################################
 ##
@@ -455,8 +444,6 @@ local func,sz,p;
   fi;
   if sz[1] in PERFRec.notKnown then
     Error("Perfect groups of size ",sz[1]," not known");
-  elif sz[1] in PERFRec.notAvailable then
-    Error("Perfect groups of size ",sz[1]," not available");
   fi;
   p:=PerfGrpLoad(sz[1]);
   if p=fail or sz[2]>PERFRec.number[p] then
@@ -490,7 +477,7 @@ local size,i,nr,n,leng,sizenum,hpnum,description,centre,orbsize;
   if IsInt(arg[1]) then
     size:=arg[1];
     if Length(arg)=1 then
-      nr:=[1..NumberPerfectLibraryGroups(size)];
+      nr:=[1..NumberPerfectGroups(size)];
     else
       nr:=arg[2];
     fi;
@@ -504,10 +491,7 @@ local size,i,nr,n,leng,sizenum,hpnum,description,centre,orbsize;
   fi;
 
   sizenum:=PerfGrpLoad(size);
-  if size in PERFRec.notAvailable then
-    Print("#I  no information available about size ",size,"\n");
-    return;
-  elif size in PERFRec.notKnown then
+  if size in PERFRec.notKnown then
     Print("#I  no information known about size ",size,"\n");
     return;
   fi;
@@ -690,11 +674,11 @@ local s,l;
   fi;
   s:=Size(G);
   PerfGrpLoad(0);
-  if s>=10^6 or s in PERFRec.notAvailable or s in PERFRec.notKnown then
+  if s>=10^6 or s in PERFRec.notKnown then
     Print("#W  No information about size ",s," available\n");
     return fail;
   fi;
-  l:=NumberPerfectLibraryGroups(s);
+  l:=NumberPerfectGroups(s);
   while l>1 do
     if IsomorphismGroups(G,PerfectGroup(IsPermGroup,s,l))<>fail then
       return [s,l];

grp/perf0.grp

@@ -8,7 +8,8 @@
 ##
 ##  SPDX-License-Identifier: GPL-2.0-or-later
 ##
-##  All data is based on Holt/Plesken: Perfect Groups, OUP 1989
+##  Data is based on Holt/Plesken: Perfect Groups, OUP 1989 and
+##  Hulpke: The perfect groups of order up to 10^6
 ##
 
 ##  The  1097  nontrivial
@@ -45,11 +46,6 @@
 ##        have  not  yet   been  determined.   It  is  needed  by  subroutine
 ##        NumberPerfectGroups.
 ##
-##     PERFRec.notAvailable
-##        is a list of all sizes less than 10^6  for which the perfect groups
-##        are known, but not yet in the library.  It is needed by subroutines
-##        DisplayInformationPerfectGroups and NumberPerfectLibraryGroups.
-##
 ##     PERFRec.sizeNumberSimpleGroup
 ##        is an ordered list of the  'size numbers'  of all nonabelian simple
 ##        groups which occur as composition factor of any library group.
@@ -140,10 +136,7 @@ PERFRec := MakeImmutable(rec(
 
  covered := [38,59,70,71,80,113,151,158,201,249,295,331],
 
- notKnown := [
- 61440,122880,172032,245760,344064,491520,688128,983040],
-
- notAvailable := [86016,368640,737280],
+ notKnown := [],
 
  nameSimpleGroup := [
  "A(5)","A(6)","A(7)","A(8)","A(9)","A5","A6","A7","A8","A9","J(1)",
@@ -215,25 +208,29 @@ PERFRec := MakeImmutable(rec(
  892800,900000,903168,907200,912576,921600,921984,929280,933120,936000,
  937500,943488,950400,950520,960000,962280,967680,976500,979200,979776,
  983040,987840],
+
+ newlyAdded:=[61440,86016,122880,172032,245760,344064,368640,491520,
+              688128,737280,983040],
 
- number := [
- 1,1,1,1,1,1,1,1,1,2,1,1,1,2,7,1,1,1,1,3,1,1,1,7,1,2,1,1,1,1,1,1,1,
- 1,2,2,1,5,1,1,3,1,1,9,4,1,1,1,1,1,1,3,1,7,1,1,1,1,5,22,1,3,1,1,1,
- 1,1,4,1,1,37,2,1,1,4,1,1,1,4,25,3,1,1,1,3,1,1,1,2,2,2,1,2,1,3,0,1,
- 4,1,1,1,4,1,4,4,3,1,1,6,1,52,1,8,2,1,3,1,1,1,1,1,1,15,3,1,1,1,4,5,
- 2,0,1,6,4,3,2,2,1,1,1,1,1,1,18,1,3,1,12,1,0,8,1,1,1,3,1,19,1,1,2,1,
- 1,1,1,1,3,1,2,1,26,3,3,1,17,5,1,1,2,0,1,1,4,3,2,7,1,1,2,1,3,2,3,1,
- 3,18,1,27,1,1,0,3,1,1,1,6,1,1,3,3,46,1,1,11,1,1,2,2,1,1,4,3,1,1,1,1,
- 3,1,2,1,1,3,8,1,1,25,4,3,18,1,4,17,6,1,0,1,1,1,1,1,9,1,1,1,1,19,1,1,
- 7,1,1,2,3,1,4,1,12,1,2,41,1,1,1,3,2,1,0,23,3,2,1,1,1,1,2,3,2,1,1,3,
- 54,1,13,2,5,3,16,2,2,1,3,2,3,3,2,1,2,1,1,3,1,7,6,4,1,23,8,2,21,3,8,1,
- 2,1,12,1,20,1,1,4,0,1],
+number:=[ 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 7, 1, 1, 1, 1, 3, 1, 1, 
+  1, 7, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 5, 1, 1, 3, 1, 1, 9, 4, 1, 1, 
+  1, 1, 1, 1, 3, 1, 7, 1, 1, 1, 1, 5, 22, 1, 3, 1, 1, 1, 1, 1, 4, 1, 1, 37, 
+  2, 1, 1, 4, 1, 1, 1, 4, 25, 3, 1, 1, 1, 3, 1, 1, 1, 2, 2, 2, 1, 2, 1, 3, 
+  98, 1, 4, 1, 1, 1, 4, 1, 4, 4, 3, 1, 1, 6, 1, 52, 1, 8, 2, 1, 3, 1, 1, 1, 
+  1, 1, 1, 15, 3, 1, 1, 1, 4, 5, 2, 258, 1, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 
+  18, 1, 3, 1, 12, 1, 154, 8, 1, 1, 1, 3, 1, 19, 1, 1, 2, 1, 1, 1, 1, 1, 3, 1, 
+  2, 1, 26, 3, 3, 1, 17, 5, 3, 1, 2, 582, 1, 1, 4, 3, 2, 7, 1, 1, 2, 1, 3, 2, 
+  3, 1, 3, 18, 1, 27, 1, 1, 291, 3, 1, 1, 1, 6, 1, 1, 3, 3, 46, 1, 1, 11, 1, 1, 
+  2, 2, 1, 1, 4, 3, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 8, 1, 1, 25, 4, 3, 18, 1, 
+  4, 17, 6, 1, 1004, 1, 1, 1, 1, 1, 9, 1, 1, 1, 1, 19, 1, 1, 7, 1, 1, 2, 3, 1, 
+  4, 1, 12, 1, 2, 41, 1, 1, 1, 3, 2, 1, 508, 23, 3, 2, 1, 1, 1, 1, 2, 3, 3, 1, 
+  1, 3, 54, 1, 13, 2, 5, 3, 16, 2, 2, 1, 3, 2, 3, 3, 3, 1, 3, 1, 1, 3, 1, 7, 
+  6, 4, 1, 23, 8, 2, 21, 3, 8, 1, 2, 1, 12, 1, 20, 1, 1, 4, 1880, 1 ],
 
 ));
 
 IsSSortedList( PERFRec.covered );
 IsSSortedList( PERFRec.notKnown );
-IsSSortedList( PERFRec.notAvailable );
 IsSSortedList( PERFRec.nameSimpleGroup );
 IsSSortedList( PERFRec.sizeNumberSimpleGroup );
 IsSSortedList( PERFRec.sizes );

grp/perf11.grp

@@ -1337,7 +1337,34 @@
   # 729000.2
   [[4,29160,6,3000,2,120,3,1],
   "A5 2^1 # 3^5 5^2 [2]",6,3,
-  1,[243,25]]
+  1,[243,25]],
+  # 729000.3
+  [[1,"abrstuvwxyz",
+  function(a,b,r,s,t,u,v,w,x,y,z)
+  return
+  [[w^2,t^3,u^3,v^3,s^3,z^3,x^-1*y^-1*x*y,b^-1*z*b*z^-1,u^-1*y*u*y^-1,
+  t*s*t^-1*s^-1,u*z^-1*u^-1*z,t^-1*z*t*z^-1,s^-1*x^-1*s*x,t^-1*x^-1*t*x,
+  t^-1*y^-1*t*y,w*z*w*z^-1,s^-1*z*s*z^-1,(w*y)^2,(w*x^-1)^2,u*x^-1*u^-1*x,
+  s^-1*w*s*w,a^-1*u*a*t^-1,v*x*v^-1*x^-1,u^-1*t^-1*u*t,a^-1*z*a*z^-1,
+  u^-1*w*u*w,v*y^-1*v^-1*y,s*v^-1*s^-1*v,s^-1*y^-1*s*y,v^-1*w*v*w,t^-1*w*t*w,
+  r^-1*z*r*z^-1,v^-1*z*v*z^-1,t^-1*v*t*v^-1,x^-1*z*x*z^-1,v^-1*u^-1*v*u,
+  s*u^-1*s^-1*u,y^-1*z*y*z^-1,z^-1*t*b^-1*u^-1*b,a*u^-1*a^-1*t*s,
+  r^-1*t^-1*r*v^-1*u,z^-1*v^-1*r*v^-1*r^-1,z^-1*u^-1*b^-1*t*b,x*r*x*r^-1*y^-1,
+  r^-1*x^-1*r*y^-1*x,x^-1*r*w*r^-1*w,a*t*s*a^-1*t^-1,a*z^-1*v^-1*a^-1*v,
+  v*r*t*r^-1*u^-1,a^-1*u*t^-1*a*s,a^-1*z^-1*v*a*v^-1,b^-1*x^-1*b*x^2,y^5,x^5,
+  w*y*b*w*x^-1*b^-1,a^-1*x*w*y^-1*a*w,w*a^-1*w*a*x*y^-1,s*z^-1*b*v^-1*u*b^-1,
+  b^-1*x^-1*y^-1*b*y^-2,a*x*y^-1*a*w*a,b^-1*v^-1*z*b*t*s,y*x^-1*y*a^-1*y*a,
+  s*r*t^-1*z^-1*u*s^-1*r^-1,s^-1*r*t*z*u^-1*s*r^-1,a*y^-2*a^-1*r^-1*y^-1*r,
+  r^-1*b^-1*r^-1*b*r*b*x^-1,a^-1*r^-1*a^-1*r*t^-1*u*s*x^-1,b^-2*u*w*t*x*y^-1*x,
+  r^-2*w*y*s*u*t^-1*y,r^-1*a*r*t*u^-1*s^-1*a*x,a^-1*r*x*t*a^-1*t^-1*s*r^-1*x^-1,
+  r^-1*a*r*x*a*r^-1*a^-1*r*a^-1,(b^-1*a^-1)^2*b*s*a^-1*x^-1*v*w,
+  (b^-1*a)^2*b*a*x*s^-1*t*y^-2],
+  [[v,w,x,y,u*t*u,t*y*s,(u^-1)^b,a*r^-1*x^-1,r*b^-1*r],
+  [s,t,u,v,w,z,x*a*y^-1,b*a^-1*y^-1,a*w^-1*r^-1]]];
+  end,
+  [18,25]],
+  "PG729000.3",[0,0,0],3,1,[18,25]]
+
   ];
   PERFGRP[287]:=[# 730800.1
   [[2,60,1,12180,1],

grp/perf12.grp

@@ -615,7 +615,10 @@
   # 871200.2
   [[3,1320,1,1320,1,"d1","d2"],
   "( L2(11) x L2(11) ) 2^1 [2]",40,2,
-  [5,5],288]
+  [5,5],288],
+  # 871200.3 (new)
+  [[2,60,1,14520,1],
+  "A5 x A5 2^1 11^2",0,1,[1,1],[5,121]]
   ];
   PERFGRP[305]:=[# 874800.1
   [[2,60,1,14580,1],
@@ -654,7 +657,19 @@
   end,
   [132]],
   "L2(11) N 11^3",[19,3,2],1,
-  5,132]
+  5,132],
+  # 878460.3 (new)
+  [[1,"abcwxyz",
+  function(a,b,c,w,x,y,z)
+  return 
+  [[b^2,c^2,a^3,y^-1*z^-1*y*z,(a*c)^2,w^-1*y^-1*w*y,w^-1*z^-1*w*z,
+  a^-1*y*a*y^-1,w^-1*x^-1*w*x,x^-1*z^-1*x*z,b*x*b*y^-1,b*z*b*z^-1,
+  x^-1*y^-1*x*y,a^-1*w*a*x^-1, c*x*c*x^-1,a^-1*z*a*z^-1,c*y*c*z^-1,
+  b*w*b*c*w^-1*c,(b*c)^3,(b*a^-1)^3,c*y*w*z*c*x*w,z^11,y^11,x^11,w^11],
+  [[a,b,x^-1*w]]];
+  end,[55]],
+  "A5 11^4",0,1,[1],55]
+
   ];
   PERFGRP[307]:=[# 881280.1
   [[2,360,1,2448,1],