> < ^ Date: Wed, 29 May 1996 17:44:05 +0200
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
^ Subject: Patch #10

Dear GAP-Forum:

This mail contains a bugfix for two serious problems in GAP 3.4.3.
You should apply this bugfix soon if you are using the primitive groups
library. One problem is that the library stored the wrong parity for two
groups. The other problem is the disability to create the last group.
Additionally, this bugfix adds new names for the groups.

HOW TO APPLY

The problem is a serious problem, because it may cause a computation to
fail. Thus the bugfix has medium priority, and we recommend that you
apply it soon if you are using the primitive groups library.

Go to the GAP directory (the directory with the 'grp/' subdirectory),
name this file 'bugfix10.dif', and issue the command:

patch -p0 < bugfix10.dif

If 'patch' writes "I can't seem to find a patch in there" try 'patch -v'.
If 'patch -v' gives an error message or reports a version older than 2.1,
get 2.1 from 'ftp://FTP.Math.RWTH-Aachen.DE/pub/gap/utils/patch2_1.zoo'.

This fix changes only the groups library. Thus you need not recompile
the GAP kernel.

VERSION

3.4.3.0

DESCRIPTION

'PrimitiveGroup(49,36)' and 'PrimitiveGroup(49,37)' are stored with
incorrect parity (i.e., with incorrect '<group>.isOdd' value).
'PrimitiveGroup(50,9)' signals 'Error, <nr> is too large' instead
of creating the group 'S(50)'.

CORRECT BEHAVIOUR

gap> g := PrimitiveGroup(49,36);;
gap> g.isOdd; SignPermGroup(g);
true
-1
gap> g := PrimitiveGroup(49,37);;
gap> g.isOdd; SignPermGroup(g);
false
1
gap> g := PrimitiveGroup(50,9);
S(50)

COMMENT

The problems were found and reported in the GAP forum by Sebastian Egner.
He also provided a 'diff' file (which unfortunately was reversed).

PATCH

Prereq: 3.1
--- grp/primitiv.grp    Thu Dec 21 15:25:52 1995
+++ grp/primitiv.grp    Wed May 29 17:19:52 1996
@@ -1,15 +1,24 @@
 #############################################################################
 ##
 #A  primitiv.grp                GAP group library                Charles Sims
+#A                                                       & Francis Buekenhout
+#A                                                          & Dimitri Leemans
 ##
-#A  @(#)$Id: 1.html,v 1.2 2004/04/21 15:04:32 felsch Exp $
+#A  @(#)$Id: 1.html,v 1.2 2004/04/21 15:04:32 felsch Exp $
 ##
 #Y  Copyright 1967-1992,  Charles Sims,  Rutgers University,  New Jersey, USA
 ##
 ##  This file contains the functions  of  the  primitive  group  library  and
-##  the primitiv groups of degree up to 50.
+##  the primitiv groups of degree up to 50 with the names given  to  them  by
+##  Buekenhout and Leemans.
 ##
 #H  $Log: 1.html,v $
 #H  Revision 1.2  2004/04/21 15:04:32  felsch
 #H  Corrected links in the Forum Archive pages.   VF
 #H
 #H  Revision 1.1.1.1  2004/04/20 13:39:35  felsch
 #H  The final GAP-Forum archive until 2003.
 #H
 #H  Revision 1.5  2003/06/12 19:20:33  gap
 #H  Further update. AH
 #H
 #H  Revision 1.4  2003/06/12 17:28:25  gap
 #H  Address updates by JN. AH
 #H
 #H  Revision 1.3  1997/08/15 11:19:33  gap
 #H  New forum setup. AH
 #H
 #H  Revision 1.2  1997/04/24 15:32:47  gap
 #H  These files were replaced by the versions in WWW. The content is basically the
 #H  same but the formatting has been much more friendly towards the HTML-Converter.
 #H  AH
 #H
 #H  Revision 1.1  1996/10/30 13:07:04  gap
 #H  added forum archive and translation files.
 #H
+#H  Revision 3.1.1.2  1996/05/29  15:12:43  mschoene
+#H  fixed an error message (problem also found be Sebastian Egner)
+#H
+#H  Revision 3.1.1.1  1996/05/28  09:20:39  ahulpke
+#H  fixed PrimitiveGroup(50,9), isOdd in 49/36,37 and added new names
+#H
 #H  Revision 3.1  1992/01/07  15:58:56  martin
 #H  initial revision under RCS
 #H
@@ -643,6 +652,7 @@
 ##  <stabilizer>:       if the stabilizer of the last point is primitive this
 ##                      is its identity,
 ##  <name>:             if known, a descriptive name for <G>,
+##                         PYL=P\Gamma L, PZL= P\Sigma L
 ##  <generators>:       a list of indices into the table 'PGGens'.
 ##
 FAC := Factorial;  EABL := 0000;
@@ -654,19 +664,19 @@
 [ 3,         6,  3, 10110, 0301, 0201,       "S(3)", 2,1],
 [ 4,        12,  2, 11010, EABL, 0301,       "A(4)", 3,2],
 [ 4,        24,  4, 10100, EABL, 0302,       "S(4)", 4,1],
-[ 5,         5,  1, 00001, 0501,     ,             , 5],
-[ 5,        10,  1, 00010, 0501,     ,             , 5,6],
-[ 5,        20,  2, 10110, 0501,     ,             , 5,7],
+[ 5,         5,  1, 00001, 0501,     ,          "5", 5],
+[ 5,        10,  1, 00010, 0501,     ,        "5:2", 5,6],
+[ 5,        20,  2, 10110, 0501,     ,        "5:4", 5,7],
 [ 5,        60,  3, 11001, 0504, 0401,       "A(5)", 8,2],
 [ 5,       120,  5, 10100, 0504, 0402,       "S(5)", 5,1],
 [ 6,        60,  2, 01001, 0601, 0502,   "PSL(2,5)", 5,6,9],
 [ 6,       120,  3, 10100, 0601, 0503,   "PGL(2,5)", 5,7,9],
 [ 6,       360,  4, 11001, 0603, 0504,       "A(6)", 10,2],
 [ 6,       720,  6, 10100, 0603, 0505,       "S(6)", 11,1],
-[ 7,         7,  1, 00001, 0701,     ,             , 12],
-[ 7,        14,  1, 00110, 0701,     ,             , 12,13],
-[ 7,        21,  1, 00010, 0701,     ,             , 12,14],
-[ 7,        42,  2, 10110, 0701,     ,             , 12,15],
+[ 7,         7,  1, 00001, 0701,     ,          "7", 12],
+[ 7,        14,  1, 00110, 0701,     ,        "7:2", 12,13],
+[ 7,        21,  1, 00010, 0701,     ,        "7:3", 12,14],
+[ 7,        42,  2, 10110, 0701,     ,   "AGL(1,7)", 12,15],
 [ 7,       168,  2, 00001, 0705,     ,   "PSL(3,2)", 12,16],
 [ 7,      2520,  5, 11001, 0706, 0603,       "A(7)", 17,2],
 [ 7,      5040,  7, 10100, 0706, 0604,       "S(7)", 12,1],
@@ -677,15 +687,15 @@
 [ 8,      1344,  3, 00000, EABL, 0705,   "ASL(3,2)", 12,16,18],
 [ 8,     20160,  6, 11001, 0806, 0706,       "A(8)", 20,2],
 [ 8,     40320,  8, 10100, 0806, 0707,       "S(8)", 21,1],
-[ 9,        36,  1, 00010, EABL,     ,             , 22,23],
-[ 9,        72,  1, 00100, EABL,     ,             , 22,23,24],
+[ 9,        36,  1, 00010, EABL,     ,      "3^2:4", 22,23],
+[ 9,        72,  1, 00100, EABL,     ,    "3^2:D_8", 22,23,24],
 [ 9,        72,  2, 10110, EABL,     ,   "AGL(1,9)", 22,25],
-[ 9,        72,  2, 10010, EABL,     ,  "<AYL(1,9)", 22,23,26],
+[ 9,        72,  2, 10010, EABL,     ,        "M_9", 22,23,26],
 [ 9,       144,  2, 00100, EABL,     ,   "AYL(1,9)", 22,25,24],
-[ 9,       216,  2, 00000, EABL,     ,    "Huppert", 22,23,27],
-[ 9,       432,  2, 00100, EABL,     ,    "Huppert", 22,25,27],
+[ 9,       216,  2, 00000, EABL,     ,"3^2:(2`A_4)", 22,23,27],
+[ 9,       432,  2, 00100, EABL,     ,   "AGL(2,3)", 22,25,27],
 [ 9,       504,  3, 11001, 0908, 0801,   "PSL(2,8)", 12,18,28],
-[ 9,      1512,  3, 01000, 0908, 0802,   "PZL(2,8)", 12,18,28,14],
+[ 9,      1512,  3, 01000, 0908, 0802,   "PYL(2,8)", 12,18,28,14],
 [ 9,  FAC(9)/2,  7, 11001, 0910, 0806,       "A(9)", 29,2],
 [ 9,    FAC(9),  9, 10100, 0910, 0807,       "S(9)", 30,1],
 [10,        60,  1, 00001, 1001,     ,       "A(5)", 31,32],
@@ -693,13 +703,13 @@
 [10,       360,  2, 01001, 1003, 0901,   "PSL(2,9)", 22,23,34],
 [10,       720,  2, 01100, 1003, 0902,       "S(6)", 22,23,24,34],
 [10,       720,  3, 10100, 1003, 0903,   "PGL(2,9)", 22,25,34],
-[10,       720,  3, 10000, 1003, 0904,  "<PYL(2,9)", 22,23,26,34],
+[10,       720,  3, 10000, 1003, 0904,       "M_10", 22,23,26,34],
 [10,      1440,  3, 00100, 1003, 0905,   "PYL(2,9)", 22,25,24,34],
 [10, FAC(10)/2,  8, 11001, 1008, 0910,      "A(10)", 35,2],
 [10,   FAC(10), 10, 00100, 1008, 0911,      "S(10)", 36,1],
-[11,        11,  1, 00001, 1101,     ,             , 37],
-[11,        22,  1, 00110, 1101,     ,             , 37,38],
-[11,        55,  1, 00010, 1101,     ,             , 37,39],
+[11,        11,  1, 00001, 1101,     ,         "11", 37],
+[11,        22,  1, 00110, 1101,     ,       "11:2", 37,38],
+[11,        55,  1, 00010, 1101,     ,       "11:5", 37,39],
 [11,       110,  2, 10110, 1101,     ,  "AGL(1,11)", 37,40],
 [11,       660,  2, 01001, 1105, 1001,  "PSL(2,11)", 31,32,41],
 [11,      7920,  4, 10001, 1106, 1006,      "M(11)", 22,23,26,34,42],
@@ -711,11 +721,11 @@
 [12,     95040,  5, 10001, 1204, 1106,      "M(12)", 22,23,26,34,42,46],
 [12, FAC(12)/2, 10, 01001, 1205, 1107,      "A(12)", 47,2],
 [12,   FAC(12), 12, 00100, 1205, 1108,      "S(12)", 48,1],
-[13,        13,  1, 00001, 1301,     ,             , 49],
-[13,        26,  1, 00010, 1301,     ,             , 49,50],
-[13,        39,  1, 00010, 1301,     ,             , 49,51],
-[13,        52,  1, 00110, 1301,     ,             , 49,52],
-[13,        78,  1, 00010, 1301,     ,             , 49,53],
+[13,        13,  1, 00001, 1301,     ,         "13", 49],
+[13,        26,  1, 00010, 1301,     ,       "13:2", 49,50],
+[13,        39,  1, 00010, 1301,     ,       "13:3", 49,51],
+[13,        52,  1, 00110, 1301,     ,       "13:4", 49,52],
+[13,        78,  1, 00010, 1301,     ,       "13:6", 49,53],
 [13,       156,  2, 10110, 1301,     ,  "AGL(1,13)", 49,54],
 [13,      5616,  2, 00001, 1307,     ,   "PSL(3,3)", 49,55],
 [13, FAC(13)/2, 11, 01001, 1308, 1205,      "A(13)", 56,2],
@@ -730,20 +740,20 @@
 [15,     20160,  2, 00001, 1504,     ,   "PSL(4,2)", 63,64],
 [15, FAC(15)/2, 13, 01001, 1505, 1403,      "A(15)", 65,2],
 [15,   FAC(15), 15, 00100, 1505, 1404,      "S(15)", 66,1],
-[16,        80,  1, 00010, EABL,     ,             , 60,67],
-[16,       160,  1, 00000, EABL,     ,             , 60,67,68],
+[16,        80,  1, 00010, EABL,     ,      "2^4:5", 60,67],
+[16,       160,  1, 00000, EABL,     ,   "2^4:D_10", 60,67,68],
 [16,       240,  2, 10010, EABL,     ,  "AGL(1,16)", 69,67],
-[16,       288,  1, 00000, EABL,     ,             , 61,67,70,71],
-[16,       320,  1, 00000, EABL,     ,             , 60,67,72],
-[16,       480,  2, 00000, EABL,     , "<AYL(1,16)", 69,67,68],
-[16,       576,  1, 00000, EABL,     ,             , 61,67,70,73],
-[16,       576,  1, 00000, EABL,     ,             , 61,67,70,71,74],
-[16,       960,  1, 00000, EABL,     ,             , 60,67,75],
+[16,       288,  1, 00000, EABL,     ,"(A_4xA_4):2", 61,67,70,71],
+[16,       320,  1, 00000, EABL,     ,  "(2^4:5).4", 60,67,72],
+[16,       480,  2, 00000, EABL,     ,"AGL(1,16):2", 69,67,68],
+[16,       576,  1, 00000, EABL,     ,  "2^4.3^2:4", 61,67,70,73],
+[16,       576,  1, 00000, EABL,     ,"2^4.S_3xS_3", 61,67,70,71,74],
+[16,       960,  1, 00000, EABL,     ,    "2^4:A_5", 60,67,75],
 [16,       960,  2, 00000, EABL,     ,  "AYL(1,16)", 69,67,72],
 [16,       960,  2, 00000, EABL,     ,   "ASL(2,4)", 60,67,70],
-[16,      1152,  1, 00000, EABL,     ,             , 61,67,70,71,76],
-[16,      1920,  1, 00000, EABL,     ,             , 60,67,77],
-[16,      1920,  2, 00000, EABL,     ,   "AZL(2,4)", 60,67,78],
+[16,      1152,  1, 00000, EABL,     ,"(S_4xS_4):2", 61,67,70,71,76],
+[16,      1920,  1, 00000, EABL,     ,    "2^4:S_5", 60,67,77],
+[16,      1920,  2, 00000, EABL,     , "ASL(2,4):2", 60,67,78],
 [16,      2880,  2, 00000, EABL,     ,   "AGL(2,4)", 69,67,70],
 [16,      5760,  2, 00000, EABL,     ,   "AYL(2,4)", 69,67,78],
 [16,      5760,  2, 01000, EABL, 1501,   "2^4.A(6)", 60,61,67],
@@ -752,13 +762,13 @@
 [16,    322560,  3, 00000, EABL, 1504, "2^4.L(4,2)", 63,64,67],
 [16, FAC(16)/2, 14, 01001, 1621, 1505,      "A(16)", 79,2],
 [16,   FAC(16), 16, 00100, 1621, 1506,      "S(16)", 80,1],
-[17,        17,  1, 00001, 1701,     ,             , 81],
-[17,        34,  1, 00010, 1701,     ,             , 81,82],
-[17,        68,  1, 00010, 1701,     ,             , 81,83],
-[17,       136,  1, 00010, 1701,     ,             , 81,84],
+[17,        17,  1, 00001, 1701,     ,         "17", 81],
+[17,        34,  1, 00010, 1701,     ,       "17:2", 81,82],
+[17,        68,  1, 00010, 1701,     ,       "17:4", 81,83],
+[17,       136,  1, 00010, 1701,     ,       "17:8", 81,84],
 [17,       272,  2, 10110, 1701,     ,  "AGL(1,17)", 81,85],
 [17,      4080,  3, 10001, 1706, 1603,  "PSL(2,16)", 69,67,86],
-[17,      8160,  3, 00000, 1706, 1606, "<PZL(2,16)", 69,67,68,86],
+[17,      8160,  3, 00000, 1706, 1606,"PSL(2,16):2", 69,67,68,86],
 [17,     16320,  3, 00000, 1706, 1610,  "PYL(2,16)", 69,67,72,86],
 [17, FAC(17)/2, 15, 01001, 1709, 1621,      "A(17)", 87,2],
 [17,   FAC(17), 17, 00100, 1709, 1622,      "S(17)", 81,1],
@@ -766,11 +776,11 @@
 [18,      4896,  3, 10100, 1801, 1705,  "PGL(2,17)", 81,85,88],
 [18, FAC(18)/2, 16, 01001, 1803, 1709,      "A(18)", 89,2],
 [18,   FAC(18), 18, 00100, 1803, 1710,      "S(18)", 90,1],
-[19,        19,  1, 00001, 1901,     ,             , 91],
-[19,        38,  1, 00110, 1901,     ,             , 91,92],
-[19,        57,  1, 00010, 1901,     ,             , 91,93],
-[19,       114,  1, 00110, 1901,     ,             , 91,94],
-[19,       171,  1, 00010, 1901,     ,             , 91,95],
+[19,        19,  1, 00001, 1901,     ,         "19", 91],
+[19,        38,  1, 00110, 1901,     ,       "19:2", 91,92],
+[19,        57,  1, 00010, 1901,     ,       "19:3", 91,93],
+[19,       114,  1, 00110, 1901,     ,       "19:6", 91,94],
+[19,       171,  1, 00010, 1901,     ,       "19:9", 91,95],
 [19,       342,  2, 10110, 1901,     ,  "AGL(1,19)", 91,96],
 [19, FAC(19)/2, 17, 01001, 1907, 1803,      "A(19)", 97,2],
 [19,   FAC(19), 19, 00100, 1907, 1804,      "S(19)", 91,1],
@@ -788,12 +798,12 @@
 [21, FAC(21)/2, 19, 11001, 2108, 2003,      "A(21)", 109,2],
 [21,   FAC(21), 21, 10100, 2108, 2004,      "S(21)", 110,1],
 [22,    443520,  3, 00001, 2201, 2104,      "M(22)", 101,106,111],
-[22,    887040,  3, 00100, 2201, 2105,             , 101,106,107,111],
+[22,    887040,  3, 00100, 2201, 2105,    "M(22):2", 101,106,107,111],
 [22, FAC(22)/2, 20, 11001, 2203, 2108,      "A(22)", 112,2],
 [22,   FAC(22), 22, 10100, 2203, 2109,      "S(22)", 113,1],
-[23,        23,  1, 00001, 2301,     ,             , 114],
-[23,        46,  1, 00110, 2301,     ,             , 114,115],
-[23,       253,  1, 00010, 2301,     ,             , 114,116],
+[23,        23,  1, 00001, 2301,     ,         "23", 114],
+[23,        46,  1, 00110, 2301,     ,       "23:2", 114,115],
+[23,       253,  1, 00010, 2301,     ,      "23:11", 114,116],
 [23,       506,  2, 10110, 2301,     ,  "AGL(1,23)", 114,117],
 [23,  10200960,  4, 00001, 2305, 2201,      "M(23)", 101,106,111,118],
 [23, FAC(23)/2, 21, 11001, 2306, 2203,      "A(23)", 119,2],
@@ -803,75 +813,75 @@
 [24, 244823040,  5, 00001, 2403, 2305,      "M(24)", 101,106,111,118,121],
 [24, FAC(24)/2, 22, 11001, 2404, 2306,      "A(24)", 122,2],
 [24,   FAC(24), 24, 10100, 2404, 2307,      "S(24)", 123,1],
-[25,        75,  1, 00010, EABL,     ,             , 124,125],
-[25,       150,  1, 00010, EABL,     ,             , 124,125,126],
-[25,       150,  1, 00000, EABL,     ,             , 124,125,127],
-[25,       200,  1, 00000, EABL,     ,             , 124,128,129],
-[25,       200,  1, 00110, EABL,     ,             , 124,130],
-[25,       200,  1, 00010, EABL,     ,             , 124,131,129],
-[25,       300,  1, 00010, EABL,     ,             , 124,125,132],
-[25,       300,  1, 00010, EABL,     ,             , 124,125,129],
-[25,       300,  1, 00000, EABL,     ,             , 124,125,126,127],
-[25,       400,  1, 00100, EABL,     ,             , 124,130,127],
-[25,       400,  1, 00000, EABL,     ,             , 124,132,128,127],
-[25,       600,  1, 00000, EABL,     ,             , 124,125,132,127],
-[25,       600,  2, 10010, EABL,     ,  "AGL(1,25)", 124,125,133],
-[25,       600,  2, 10110, EABL,     , "<AYL(1,25)", 124,125,130],
-[25,       600,  2, 10110, EABL,     ,    "Huppert", 124,125,134],
-[25,       800,  1, 00100, EABL,     ,             , 124,130,135],
-[25,      1200,  2, 00000, EABL,     ,  "AYL(1,25)", 124,125,133,136],
-[25,      1200,  2, 00100, EABL,     ,    "Huppert", 124,125,130,127],
-[25,      2400,  2, 00100, EABL,     ,    "Huppert", 124,125,133,137],
+[25,        75,  1, 00010, EABL,     ,      "5^2:3", 124,125],
+[25,       150,  1, 00010, EABL,     ,      "5^2:6", 124,125,126],
+[25,       150,  1, 00000, EABL,     ,    "5^2:S_3", 124,125,127],
+[25,       200,  1, 00000, EABL,     ,    "5^2:D_8", 124,128,129],
+[25,       200,  1, 00110, EABL,     ,      "5^2:8", 124,130],
+[25,       200,  1, 00010, EABL,     ,    "5^2:Q_8", 124,131,129],
+[25,       300,  1, 00010, EABL,     ,     "5^2:12", 124,125,132],
+[25,       300,  1, 00010, EABL,     ,"5^2:Q_12 ??", 124,125,129],
+[25,       300,  1, 00000, EABL,     ,   "5^2:D_12", 124,125,126,127],
+[25,       400,  1, 00100, EABL,     ,    "5^2:8:2", 124,130,127],
+[25,       400,  1, 00000, EABL,     ,  "5^2:D_8:2", 124,132,128,127],
+[25,       600,  1, 00000, EABL,     ,  "5^2:4xD_6", 124,125,132,127],
+[25,       600,  2, 10010, EABL,     ,"5^2:(Q_8:3)", 124,125,133],
+[25,       600,  2, 10110, EABL,     ,  "AGL(1,25)", 124,125,130],
+[25,       600,  2, 10110, EABL,     ,    "5^2:3:8", 124,125,134],
+[25,       800,  1, 00100, EABL,     ,"5^2:O_2+(5)", 124,130,135],
+[25,      1200,  2, 00000, EABL,     ,"5^2:((Q_8:3)`2)", 124,125,133,136],
+[25,      1200,  2, 00100, EABL,     ,   "AYL(2,5)", 124,125,130,127],
+[25,      2400,  2, 00100, EABL,     ,"5^2:((Q_8:3)`4)", 124,125,133,137],
 [25,      3000,  2, 00000, EABL,     ,   "ASL(2,5)", 124,125,138],
-[25,      6000,  2, 00000, EABL,     ,  "<AGL(2,5)", 124,125,127,138],
-[25,      7200,  1, 00000,     ,     ,             , 127,139,140],
+[25,      6000,  2, 00000, EABL,     , "ASL(2,5):2", 124,125,127,138],
+[25,      7200,  1, 00000,     ,     ,"(A_5xA_5):2", 127,139,140],
 [25,     12000,  2, 00100, EABL,     ,   "AGL(2,5)", 124,125,135,138],
-[25,     14400,  1, 00000,     ,     ,             , 127,139,140,141],
-[25,     14400,  1, 00100,     ,     ,             , 139,140,142],
-[25,     28800,  1, 00100,     ,     ,             , 127,139,140,142],
+[25,     14400,  1, 00000,     ,     ,"(A_5xA_5):2^2", 127,139,140,141],
+[25,     14400,  1, 00100,     ,     ,"(A_5xA_5):4", 139,140,142],
+[25,     28800,  1, 00100,     ,     ,"(S_5xS_5):2", 127,139,140,142],
 [25, FAC(25)/2, 23, 11001, 2527, 2404,      "A(25)", 143,2],
 [25,   FAC(25), 25, 10100, 2527, 2405,      "S(25)", 144,1],
 [26,      7800,  2, 01001, 2601, 2507,  "PSL(2,25)", 124,125,132,145],
 [26,     15600,  2, 01000, 2601, 2512,  "PZL(2,25)", 124,125,132,127,145],
 [26,     15600,  3, 10100, 2601, 2514,  "PGL(2,25)", 124,125,130,145],
-[26,     15600,  3, 10100, 2601, 2515, "<PYL(2,25)", 124,125,134,145],
+[26,     15600,  3, 10100, 2601, 2515,"PSL(2,25).2", 124,125,134,145],
 [26,     31200,  3, 00100, 2601, 2518,  "PYL(2,25)", 124,125,130,127,145],
 [26, FAC(26)/2, 24, 11001, 2606, 2527,      "A(26)", 146,2],
 [26,   FAC(26), 26, 10100, 2606, 2528,      "S(26)", 147,1],
-[27,       324,  1, 00000, EABL,     ,             , 148,149,150],
-[27,       351,  1, 00010, EABL,     ,             , 148,151],
-[27,       648,  1, 00000, EABL,     ,             , 148,149,150,152],
-[27,       648,  1, 00100, EABL,     ,             , 148,149,153],
-[27,       648,  1, 00100, EABL,     ,             , 148,149,150,154],
+[27,       324,  1, 00000, EABL,     ,    "3^3.A_4", 148,149,150],
+[27,       351,  1, 00010, EABL,     ,     "3^3:13", 148,151],
+[27,       648,  1, 00000, EABL,     , "3^3(A_4x2)", 148,149,150,152],
+[27,       648,  1, 00100, EABL,     ,    "3^3.S_4", 148,149,153],
+[27,       648,  1, 00100, EABL,     ,  "3^3.2.A_4", 148,149,150,154],
 [27,       702,  2, 10110, EABL,     ,  "AGL(1,27)", 148,151,155],
-[27,      1053,  1, 00000, EABL,     ,             , 148,151,156],
-[27,      1296,  1, 00100, EABL,     ,             , 148,149,153,154],
+[27,      1053,  1, 00000, EABL,     ,   "3^3.13.3", 148,151,156],
+[27,      1296,  1, 00100, EABL,     , "3^3(S_4x2)", 148,149,153,154],
 [27,      2106,  2, 00100, EABL,     ,  "AYL(1,27)", 148,151,157],
 [27,     25920,  1, 00001, 2710,     ,   "PSp(4,3)", 158,159],
-[27,     51840,  1, 00000, 2710,     ,             , 158,159,160],
+[27,     51840,  1, 00000, 2710,     , "PSp(4,3):2", 158,159,160],
 [27,    151632,  2, 00000, EABL,     ,   "ASL(3,3)", 148,149,151],
-[27,    303264,  2, 00100, EABL,     ,   "AZL(3,3)", 148,153,151],
+[27,    303264,  2, 00100, EABL,     ,   "AGL(3,3)", 148,153,151],
 [27, FAC(27)/2, 25, 11001, 2714, 2606,      "A(27)", 161,2],
 [27,   FAC(27), 27, 10100, 2714, 2607,      "S(27)", 162,1],
 [28,       336,  1, 00000,     ,     ,   "PGL(2,7)", 163,164,165],
 [28,       504,  1, 00001, 2802,     ,   "PSL(2,8)", 166,167],
-[28,      1512,  2, 00000, 2802,     ,   "PZL(2,8)", 166,167,168],
+[28,      1512,  2, 00000, 2802,     ,   "PYL(2,8)", 166,167,168],
 [28,      6048,  2, 00001, 2804,     , "PSU(3,3^2)", 169,170],
 [28,      9828,  2, 01001, 2805, 2702,  "PSL(2,27)", 148,151,171],
-[28,     12096,  2, 00000, 2804,     , "PZU(3,3^2)", 169,170,172],
+[28,     12096,  2, 00000, 2804,     , "PYU(3,3^2)", 169,170,172],
 [28,     19656,  3, 10100, 2805, 2706,  "PGL(2,27)", 148,151,155,171],
 [28,     20160,  1, 00001, 2808,     ,       "A(8)", 163,173],
-[28,     29484,  2, 01000, 2805, 2707,  "PZL(2,27)", 148,151,156,171],
+[28,     29484,  2, 01000, 2805, 2707,"PSL(2,27):3", 148,151,156,171],
 [28,     40320,  1, 00000, 2808,     ,       "S(8)", 163,174],
 [28,     58968,  3, 00100, 2805, 2709,  "PYL(2,27)", 148,151,157,171],
 [28,   1451520,  2, 01001, 2812, 2711,   "PSp(6,2)", 158,159,160,175],
 [28, FAC(28)/2, 26, 11001, 2813, 2714,      "A(28)", 176,2],
 [28,   FAC(28), 28, 10100, 2813, 2715,      "S(28)", 177,1],
-[29,        29,  1, 00001, 2901,     ,             , 178],
-[29,        58,  1, 00010, 2901,     ,             , 178,179],
-[29,       116,  1, 00110, 2901,     ,             , 178,180],
-[29,       203,  1, 00010, 2901,     ,             , 178,181],
-[29,       406,  1, 00010, 2901,     ,             , 178,182],
+[29,        29,  1, 00001, 2901,     ,         "29", 178],
+[29,        58,  1, 00010, 2901,     ,       "29:2", 178,179],
+[29,       116,  1, 00110, 2901,     ,       "29:4", 178,180],
+[29,       203,  1, 00010, 2901,     ,       "29:7", 178,181],
+[29,       406,  1, 00010, 2901,     ,      "29:14", 178,182],
 [29,       812,  2, 10110, 2901,     ,  "AGL(1,29)", 178,183],
 [29, FAC(29)/2, 27, 11001, 2907, 2813,      "A(29)", 184,2],
 [29,   FAC(29), 29, 10100, 2907, 2814,      "S(29)", 178,1],
@@ -879,14 +889,14 @@
 [30,     24360,  3, 10100, 3001, 2906,  "PGL(2,29)", 178,183,185],
 [30, FAC(30)/2, 28, 11001, 3003, 2907,      "A(30)", 186,2],
 [30,   FAC(30), 30, 10100, 3003, 2908,      "S(30)", 187,1],
-[31,        31,  1, 00001, 3101,     ,             , 188],
-[31,        62,  1, 00110, 3101,     ,             , 188,189],
-[31,        93,  1, 00010, 3101,     ,             , 188,190],
-[31,       155,  1, 00010, 3101,     ,             , 188,191],
-[31,       186,  1, 00110, 3101,     ,             , 188,192],
-[31,       310,  1, 00110, 3101,     ,             , 188,193],
-[31,       465,  1, 00010, 3101,     ,             , 188,194],
-[31,       930,  2, 10110, 3101,     ,             , 188,195],
+[31,        31,  1, 00001, 3101,     ,         "31", 188],
+[31,        62,  1, 00110, 3101,     ,       "31:2", 188,189],
+[31,        93,  1, 00010, 3101,     ,       "31:3", 188,190],
+[31,       155,  1, 00010, 3101,     ,       "31:5", 188,191],
+[31,       186,  1, 00110, 3101,     ,       "31:6", 188,192],
+[31,       310,  1, 00110, 3101,     ,      "31:10", 188,193],
+[31,       465,  1, 00010, 3101,     ,      "31:15", 188,194],
+[31,       930,  2, 10110, 3101,     ,  "AGL(1,31)", 188,195],
 [31,    372000,  2, 00001, 3109,     ,   "PSL(3,5)", 188,190,196],
 [31,   9999360,  2, 00001, 3110,     ,   "PSL(5,2)", 188,191,197],
 [31, FAC(31)/2, 29, 11001, 3111, 3003,      "A(31)", 198,2],
@@ -899,7 +909,7 @@
 [32, FAC(32)/2, 30, 11001, 3206, 3111,      "A(32)", 201,2],
 [32,   FAC(32), 32, 10100, 3206, 3112,      "S(32)", 202,1],
 [33,     32736,  3, 11001, 3301, 3201,  "PSL(2,32)", 188,199,203],
-[33,    163680,  3, 01000, 3301, 3202,  "PZL(2,32)", 188,191,199,203],
+[33,    163680,  3, 01000, 3301, 3202,  "PYL(2,32)", 188,191,199,203],
 [33, FAC(33)/2, 31, 11001, 3303, 3206,      "A(33)", 204,2],
 [33,   FAC(33), 33, 10100, 3303, 3207,      "S(33)", 205,1],
 [34, FAC(34)/2, 32, 11001, 3401, 3303,      "A(34)", 206,2],
@@ -911,36 +921,36 @@
 [35, FAC(35)/2, 33, 11001, 3505, 3401,      "A(35)", 213,2],
 [35,   FAC(35), 35, 10100, 3505, 3402,      "S(35)", 214,1],
 [36,       504,  1, 00001, 3601,     ,   "PSL(2,8)", 215,216,217],
-[36,       720,  1, 00100,     ,     ,             , 218,219,220],
-[36,       720,  1, 00100,     ,     ,             , 218,221,222,220],
-[36,      1440,  1, 00100,     ,     ,             , 218,219,223,220],
-[36,      1512,  1, 00000, 3601,     ,             , 215,216,217,224],
+[36,       720,  1, 00100,     ,     ,   "PGL(2,9)", 218,219,220],
+[36,       720,  1, 00100,     ,     ,       "M_10", 218,221,222,220],
+[36,      1440,  1, 00100,     ,     ,   "PYL(2,9)", 218,219,223,220],
+[36,      1512,  1, 00000, 3601,     ,   "PYL(2,8)", 215,216,217,224],
 [36,      6048,  1, 00001, 3606,     , "PSU(3,3^2)", 225,226,227,228],
-[36,      7200,  1, 00100,     ,     ,             , 229,230,231],
-[36,     12096,  1, 00000, 3606,     ,             , 225,226,227,232,228],
-[36,     14400,  1, 00100,     ,     ,             , 229,230,233],
-[36,     14400,  1, 00100,     ,     ,             , 229,230,231,234],
+[36,      7200,  1, 00100,     ,     ,"(A_5xA_5):2", 229,230,231],
+[36,     12096,  1, 00000, 3606,     , "PYU(3,3^2)", 225,226,227,232,228],
+[36,     14400,  1, 00100,     ,     ,"((A_5xA_5):2)2", 229,230,233],
+[36,     14400,  1, 00100,     ,     ,"(A_5xA_5).4", 229,230,231,234],
 [36,     25920,  1, 00001, 3611,     ,   "PSp(4,3)", 235,236],
-[36,     28800,  1, 00100,     ,     ,             , 229,230,231,233],
-[36,     51840,  1, 00000, 3611,     ,             , 235,236,237],
+[36,     28800,  1, 00100,     ,     ,"(S_5xS_5):2", 229,230,231,233],
+[36,     51840,  1, 00000, 3611,     , "PSp(4,3):2", 235,236,237],
 [36,    181440,  1, 00001, 3614,     ,       "A(9)", 238,239],
-[36,    259200,  1, 00100,     ,     ,             , 240,241,242],
+[36,    259200,  1, 00100,     ,     ,"(A_6xA_6):2", 240,241,242],
 [36,    362880,  1, 00100, 3614,     ,       "S(9)", 238,243],
-[36,    518400,  1, 00100,     ,     ,             , 240,241,244],
-[36,    518400,  1, 00100,     ,     ,             , 240,241,242,245],
-[36,   1036800,  1, 00100,     ,     ,             , 240,241,242,244],
+[36,    518400,  1, 00100,     ,     ,"(A_6xA_6):4", 240,241,244],
+[36,    518400,  1, 00100,     ,     ,"(A_6xA_6):2^2", 240,241,242,245],
+[36,   1036800,  1, 00100,     ,     ,"(S_6xS_6):2", 240,241,242,244],
 [36,   1451520,  2, 01001, 3620, 3504,   "PSp(6,2)", 208,212,246],
 [36, FAC(36)/2, 34, 11001, 3621, 3505,      "A(36)", 247,2],
 [36,   FAC(36), 36, 10100, 3621, 3506,      "S(36)", 248,1],
-[37,        37,  1, 00001, 3701,     ,             , 249],
-[37,        74,  1, 00010, 3701,     ,             , 249,250],
-[37,       111,  1, 00010, 3701,     ,             , 249,251],
-[37,       148,  1, 00110, 3701,     ,             , 249,252],
-[37,       222,  1, 00010, 3701,     ,             , 249,253],
-[37,       333,  1, 00010, 3701,     ,             , 249,254],
-[37,       444,  1, 00110, 3701,     ,             , 249,255],
-[37,       666,  1, 00010, 3701,     ,             , 249,256],
-[37,      1332,  2, 10110, 3701,     ,             , 249,257],
+[37,        37,  1, 00001, 3701,     ,         "37", 249],
+[37,        74,  1, 00010, 3701,     ,       "37:2", 249,250],
+[37,       111,  1, 00010, 3701,     ,       "37:3", 249,251],
+[37,       148,  1, 00110, 3701,     ,       "37:4", 249,252],
+[37,       222,  1, 00010, 3701,     ,       "37:6", 249,253],
+[37,       333,  1, 00010, 3701,     ,       "37:9", 249,254],
+[37,       444,  1, 00110, 3701,     ,      "37:12", 249,255],
+[37,       666,  1, 00010, 3701,     ,      "37:18", 249,256],
+[37,      1332,  2, 10110, 3701,     ,  "AGL(1,37)", 249,257],
 [37, FAC(37)/2, 35, 11001, 3710, 3621,      "A(37)", 258,2],
 [37,   FAC(37), 37, 10100, 3710, 3622,      "S(37)", 249,1],
 [38,     25308,  2, 01001, 3801, 3708,  "PSL(2,37)", 249,256,259],
@@ -951,108 +961,108 @@
 [39,   FAC(39), 39, 10100, 3901, 3804,      "S(39)", 263,1],
 [40,     25920,  1, 00001, 4001,     ,   "PSp(4,3)", 264,265],
 [40,     25920,  1, 00001, 4002,     ,   "PSp(4,3)", 266,267],
-[40,     51840,  1, 00000, 4001,     ,             , 264,265,268],
-[40,     51840,  1, 00100, 4002,     ,             , 266,267,269],
+[40,     51840,  1, 00000, 4001,     , "PSp(4,3):2", 264,265,268],
+[40,     51840,  1, 00100, 4002,     , "PSp(4,3):2", 266,267,269],
 [40,   6065280,  2, 00001, 4005,     ,   "PSL(4,3)", 270,271],
 [40,  12130560,  2, 00100, 4005,     ,   "PGL(4,3)", 270,271,272],
 [40, FAC(40)/2, 38, 11001, 4007, 3901,      "A(40)", 273,2],
 [40,   FAC(40), 40, 10100, 4007, 3902,      "S(40)", 274,1],
-[41,        41,  1, 00001, 4101,     ,             , 275],
-[41,        82,  1, 00010, 4101,     ,             , 275,276],
-[41,       164,  1, 00010, 4101,     ,             , 275,277],
-[41,       205,  1, 00010, 4101,     ,             , 275,278],
-[41,       328,  1, 00110, 4101,     ,             , 275,279],
-[41,       410,  1, 00010, 4101,     ,             , 275,280],
-[41,       820,  1, 00010, 4101,     ,             , 275,281],
-[41,      1640,  2, 10110, 4101,     ,  "AYL(1,41)", 275,282],
+[41,        41,  1, 00001, 4101,     ,         "41", 275],
+[41,        82,  1, 00010, 4101,     ,       "41:2", 275,276],
+[41,       164,  1, 00010, 4101,     ,       "41:4", 275,277],
+[41,       205,  1, 00010, 4101,     ,       "41:5", 275,278],
+[41,       328,  1, 00110, 4101,     ,       "41:8", 275,279],
+[41,       410,  1, 00010, 4101,     ,      "41:10", 275,280],
+[41,       820,  1, 00010, 4101,     ,      "41:20", 275,281],
+[41,      1640,  2, 10110, 4101,     ,  "AGL(1,41)", 275,282],
 [41, FAC(41)/2, 39, 11001, 4109, 4007,      "A(41)", 283,2],
 [41,   FAC(41), 41, 10100, 4109, 4008,      "S(41)", 275,1],
 [42,     34440,  2, 01001, 4201, 4107,  "PSL(2,41)", 275,281,284],
 [42,     68880,  3, 10100, 4201, 4108,  "PGL(2,41)", 275,282,284],
 [42, FAC(42)/2, 40, 11001, 4203, 4109,      "A(42)", 285,2],
 [42,   FAC(42), 42, 10100, 4203, 4110,      "S(42)", 286,1],
-[43,        43,  1, 00001, 4301,     ,             , 287],
-[43,        86,  1, 00110, 4301,     ,             , 287,288],
-[43,       129,  1, 00010, 4301,     ,             , 287,289],
-[43,       258,  1, 00110, 4301,     ,             , 287,290],
-[43,       301,  1, 00010, 4301,     ,             , 287,291],
-[43,       602,  1, 00110, 4301,     ,             , 287,292],
-[43,       903,  1, 00010, 4301,     ,             , 287,293],
-[43,      1806,  2, 10110, 4301,     ,  "AYL(1,43)", 287,294],
+[43,        43,  1, 00001, 4301,     ,         "43", 287],
+[43,        86,  1, 00110, 4301,     ,       "43:2", 287,288],
+[43,       129,  1, 00010, 4301,     ,       "43:3", 287,289],
+[43,       258,  1, 00110, 4301,     ,       "43:6", 287,290],
+[43,       301,  1, 00010, 4301,     ,       "43:7", 287,291],
+[43,       602,  1, 00110, 4301,     ,      "43:14", 287,292],
+[43,       903,  1, 00010, 4301,     ,      "43:21", 287,293],
+[43,      1806,  2, 10110, 4301,     ,  "AGL(1,43)", 287,294],
 [43, FAC(43)/2, 41, 11001, 4309, 4203,      "A(43)", 295,2],
 [43,   FAC(43), 43, 10100, 4309, 4204,      "S(43)", 287,1],
 [44,     39732,  2, 01001, 4401, 4307,  "PSL(2,43)", 287,293,296],
 [44,     79464,  3, 10100, 4401, 4308,  "PGL(2,43)", 287,294,296],
 [44, FAC(44)/2, 42, 11001, 4403, 4309,      "A(44)", 297,2],
 [44,   FAC(44), 44, 10100, 4403, 4310,      "S(44)", 298,1],
-[45,       720,  1, 00000,     ,     ,             , 299,300,301],
-[45,       720,  1, 00000,     ,     ,             , 299,302,303,301],
-[45,      1440,  1, 00000,     ,     ,             , 299,300,304,301],
+[45,       720,  1, 00000,     ,     ,   "PGL(2,9)", 299,300,301],
+[45,       720,  1, 00000,     ,     ,       "M_10", 299,302,303,301],
+[45,      1440,  1, 00000,     ,     ,   "PYL(2,9)", 299,300,304,301],
 [45,     25920,  1, 00001, 4504,     ,   "PSp(4,3)", 305,306],
-[45,     51840,  1, 00100, 4504,     ,             , 305,306,307],
+[45,     51840,  1, 00100, 4504,     , "PSp(4,3):2", 305,306,307],
 [45,   1814400,  1, 00001, 4506,     ,      "A(10)", 308,309],
 [45,   3628800,  1, 00000, 4506,     ,      "S(10)", 308,309,310],
 [45, FAC(45)/2, 43, 11001, 4508, 4403,      "A(45)", 311,2],
 [45,   FAC(45), 45, 10100, 4508, 4404,      "S(45)", 312,1],
 [46, FAC(46)/2, 44, 11001, 4601, 4508,      "A(46)", 313,2],
 [46,   FAC(46), 46, 10100, 4601, 4509,      "S(46)", 314,1],
-[47,        47,  1, 00001, 4701,     ,             , 315],
-[47,        94,  1, 00110, 4701,     ,             , 315,316],
-[47,      1081,  1, 00010, 4701,     ,             , 315,317],
-[47,      2162,  2, 10110, 4701,     ,             , 315,318],
+[47,        47,  1, 00001, 4701,     ,         "47", 315],
+[47,        94,  1, 00110, 4701,     ,       "47:2", 315,316],
+[47,      1081,  1, 00010, 4701,     ,      "47:23", 315,317],
+[47,      2162,  2, 10110, 4701,     ,  "AGL(1,47)", 315,318],
 [47, FAC(47)/2, 45, 11001, 4705, 4601,      "A(47)", 319,2],
 [47,   FAC(47), 47, 10100, 4705, 4602,      "S(47)", 315,1],
 [48,     51888,  2, 01001, 4801, 4703,  "PSL(2,47)", 315,317,320],
 [48,    103776,  3, 10100, 4801, 4704,  "PGL(2,47)", 315,318,320],
 [48, FAC(48)/2, 46, 11001, 4803, 4705,      "A(48)", 321,2],
 [48,   FAC(48), 48, 10100, 4803, 4706,      "S(48)", 322,1],
-[49,       196,  1, 00010, EABL,     ,             , 323,324],
-[49,       294,  1, 00100, EABL,     ,             , 323,325,326],
-[49,       392,  1, 00010, EABL,     ,             , 323,327],
-[49,       392,  1, 00010, EABL,     ,             , 323,324,328],
-[49,       392,  1, 00100, EABL,     ,             , 323,324,329],
-[49,       588,  1, 00010, EABL,     ,             , 323,325,324],
-[49,       588,  1, 00010, EABL,     ,             , 323,330,324],
-[49,       588,  1, 00100, EABL,     ,             , 323,325,331,326],
-[49,       784,  1, 00010, EABL,     ,             , 323,327,328],
-[49,       784,  1, 00110, EABL,     ,             , 323,332],
-[49,       784,  1, 00100, EABL,     ,             , 323,327,329],
-[49,       882,  1, 00100, EABL,     ,             , 323,333,326],
-[49,      1176,  1, 00010, EABL,     ,             , 323,330,327],
-[49,      1176,  1, 00010, EABL,     ,             , 323,330,324,328],
-[49,      1176,  1, 00010, EABL,     ,             , 323,324,328,334],
-[49,      1176,  1, 00000, EABL,     ,             , 323,324,328,335],
-[49,      1176,  1, 00100, EABL,     ,             , 323,325,329,326],
-[49,      1176,  1, 00100, EABL,     ,             , 323,330,324,329],
-[49,      1568,  1, 00100, EABL,     ,             , 323,332,329],
-[49,      1764,  1, 00000, EABL,     ,             , 323,333,324],
-[49,      1764,  1, 00100, EABL,     ,             , 323,333,331,326],
-[49,      2352,  2, 10010, EABL,     ,  "AGL(1,49)", 323,327,328,334],
-[49,      2352,  2, 10010, EABL,     , "<AYL(1,49)", 323,330,327,328],
-[49,      2352,  2, 10110, EABL,     ,    "Huppert", 323,330,332],
-[49,      2352,  1, 00100, EABL,     ,             , 323,330,327,329],
-[49,      3528,  1, 00000, EABL,     ,             , 323,330,328,324,334],
-[49,      3528,  1, 00100, EABL,     ,             , 323,333,329,326],
+[49,       196,  1, 00010, EABL,     ,      "7^2:4", 323,324],
+[49,       294,  1, 00100, EABL,     ,    "7^2:S_3", 323,325,326],
+[49,       392,  1, 00010, EABL,     ,      "7^2:8", 323,327],
+[49,       392,  1, 00010, EABL,     ,    "7^2:Q_8", 323,324,328],
+[49,       392,  1, 00100, EABL,     ,    "7^2:D_8", 323,324,329],
+[49,       588,  1, 00010, EABL,     ,   "7^2:Q_12", 323,325,324],
+[49,       588,  1, 00010, EABL,     ,     "7^2:12", 323,330,324],
+[49,       588,  1, 00100, EABL,     ,   "7^2:D_12", 323,325,331,326],
+[49,       784,  1, 00010, EABL,     ,   "7^2:Q_16", 323,327,328],
+[49,       784,  1, 00110, EABL,     ,     "7^2:16", 323,332],
+[49,       784,  1, 00100, EABL,     ,   "7^2:D_16", 323,327,329],
+[49,       882,  1, 00100, EABL,     ,  "7^2:3xD_6", 323,333,326],
+[49,      1176,  1, 00010, EABL,     ,     "7^2:24", 323,330,327],
+[49,      1176,  1, 00010, EABL,     ,  "7^2:3xQ_8", 323,330,324,328],
+[49,      1176,  1, 00010, EABL,     ,  "7^2:Q_8:3", 323,324,328,334],
+[49,      1176,  1, 00000, EABL,     ,  "7^2:Q_8:3", 323,324,328,335],
+[49,      1176,  1, 00100, EABL,     ,  "7^2:3:D_8", 323,325,329,326],
+[49,      1176,  1, 00100, EABL,     ,  "7^2:3xD_8", 323,330,324,329],
+[49,      1568,  1, 00100, EABL,     , "7^2:Q_16:2", 323,332,329],
+[49,      1764,  1, 00000, EABL,     , "7^2:3xQ_12", 323,333,324],
+[49,      1764,  1, 00100, EABL,     , "7^2:3xD_12", 323,333,331,326],
+[49,      2352,  2, 10010, EABL,     ,"7^2:(Q_8`D_6)", 323,327,328,334],
+[49,      2352,  2, 10010, EABL,     ,"7^2:(3xQ_16)", 323,330,327,328],
+[49,      2352,  2, 10110, EABL,     ,  "AGL(1,49)", 323,330,332],
+[49,      2352,  1, 00100, EABL,     , "7^2:3xD_16", 323,330,327,329],
+[49,      3528,  1, 00000, EABL,     ,"7^2:3x(Q_8:3)", 323,330,328,324,334],
+[49,      3528,  1, 00100, EABL,     ,"(AGL(1,7)^2):2", 323,333,329,326],
 [49,      4704,  2, 00100, EABL,     ,  "AYL(1,49)", 323,330,332,329],
-[49,      7056,  2, 00000, EABL,     ,    "Huppert", 323,330,328,327,334],
+[49,      7056,  2, 00000, EABL,     ,"7^2:((Q_8`D_6)x3)", 323,330,328,327,334],
 [49,     16464,  2, 00000, EABL,     ,   "ASL(2,7)", 323,336,324],
-[49,     32928,  2, 00100, EABL,     ,  ">ASL(2,7)", 323,336,324,326],
-[49,     49392,  2, 00000, EABL,     ,  ">ASL(2,7)", 323,336,324,330],
-[49,     56448,  1, 00100,     ,     ,             , 337,338,326],
+[49,     32928,  2, 00100, EABL,     , "ASL(2,7):2", 323,336,324,326],
+[49,     49392,  2, 00000, EABL,     , "ASL(2,7):3", 323,336,324,330],
+[49,     56448,  1, 00100,     ,     ,"(PSL(3,2)^2):2", 337,338,326],
 [49,     98784,  2, 00100, EABL,     ,   "AGL(2,7)", 323,336,324,326,330],
-[49,  12700800,  1, 00100,     ,     ,             , 339,340,326],
-[49,  25401600,  1, 00000,     ,     ,             , 339,340,326,341],
-[49,  25401600,  1, 00100,     ,     ,             , 339,340,342],
-[49,  50803200,  1, 00100,     ,     ,             , 339,340,326,343],
+[49,  12700800,  1, 00100,     ,     ,"(A_7xA_7):2", 339,340,326],
+[49,  25401600,  1, 00100,     ,     ,"(A_7xA_7):2^2", 339,340,326,341],
+[49,  25401600,  1, 00000,     ,     ,"(A_7xA_7):4", 339,340,342],
+[49,  50803200,  1, 00100,     ,     ,"(S_7xS_7):2", 339,340,326,343],
 [49, FAC(49)/2, 47, 11001, 4939, 4803,      "A(49)", 344,2],
 [49,   FAC(49), 49, 10100, 4939, 4804,      "S(49)", 345,1],
 [50,     58800,  2, 01001, 5001, 4913,  "PSL(2,49)", 323,330,327,346],
 [50,    117600,  3, 10000, 5001, 4922,  "PGL(2,49)", 323,330,327,328,346],
-[50,    117600,  3, 10100, 5001, 4924,             , 323,330,332,346],
-[50,    117600,  2, 01100, 5001, 4925,             , 323,330,327,329,346],
+[50,    117600,  3, 10100, 5001, 4924,"PSL(2,49):2", 323,330,332,346],
+[50,    117600,  2, 01100, 5001, 4925,"PSL(2,49):2", 323,330,327,329,346],
 [50,    126000,  1, 00001, 5005,     , "PSU(3,5^2)", 347,348,349,350],
-[50,    235200,  3, 00100, 5001, 4928,             , 323,330,332,329,346],
-[50,    252000,  1, 00000, 5005,     ,             , 351,348,349,350],
+[50,    235200,  3, 00100, 5001, 4928,  "PYL(2,49)", 323,330,332,329,346],
+[50,    252000,  1, 00000, 5005,     ,"PSU(3,5^2):2", 351,348,349,350],
 [50, FAC(50)/2, 48, 11001, 5008, 4939,      "A(50)", 352,2],
 [50,   FAC(50), 50, 10100, 5008, 4940,      "S(50)", 353,1]

@@ -1107,11 +1117,10 @@
     od;

     # check the number
-    if Length(PGTable) < deg  then
+    if PGTable[ Length(PGTable) ][1] < deg  then
         Error("<deg> is too large");
     fi;
-    if not IsBound( PGTable[h+nr] )
-        or PGTable[h+nr-1][1] <> deg  then
+    if not IsBound( PGTable[h+nr-1] ) or PGTable[h+nr-1][1] <> deg  then
         Error("<nr> is too large");
     fi;

@@ -1155,7 +1164,7 @@
                 fi;
             od;
             inds := inds2;  grps := grps2;
-
+
         # special case for Size
         elif arg[2*i-1] = Size  then

@@ -1292,7 +1301,7 @@
                 fi;

                 res := arg[2*i-1](grp);
-                hasProps := hasProps
+                hasProps := hasProps
                     and (res = arg[2*i]
                         or (IsList(arg[2*i])
                             and res in arg[2*i]));
@@ -1302,7 +1311,7 @@
             i := i + 1;

         od; # run over the properties
-
+
         # if the group has all properties, return it
         if hasProps  then
             if IsInt(grp)  then
END OF  bugfix10.dif ________________________________________________________

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