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<title> Changes in the GAP Character Table Library</title>
<h1 align="center">Changes in the GAP Character Table Library </h1>
<div class="p"><!----></div>
<br /><br /> <body bgcolor="FFFFFF">
<div class="p"><!----></div>
This list contains the changes in the <font face="helvetica"><font size="+0">GAP</font></font> character table library
since the official upgrade for <font face="helvetica"><font size="+0">GAP</font></font> 3.4 in October 1996.
We denote mathematical errors by <b>***</b> and new information
by <b>NEW</b>.
We use <b>C</b> to denote changes that are not obviously corrections;
the number of these changes is kept small.
<div class="p"><!----></div>
<br /><br /><b>Release of <font face="helvetica"><font size="+0">GAP</font></font> 4.1 in July 1999</b>
<div class="p"><!----></div>
<br /><br /><b>Brauer Tables</b>
<div class="p"><!----></div>
Changes are assigned to the simple group involved,
and shown in alphabetical order.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> <sup>2</sup>E<sub>6</sub>(2)</td><td valign="top"> : </td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The faithful characters of 2.<sup>2</sup>E<sub>6</sub>(2) and
2.<sup>2</sup>E<sub>6</sub>(2).2 mod 19 were corrected
(contributed by Jürgen Müller).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> A<sub>13</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
Indicators of A<sub>13</sub> and S<sub>13</sub> mod 2 are now known.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> A<sub>14</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of A<sub>14</sub> mod 2, 11, 13 and
tables of S<sub>14</sub> mod 3, 5, 7 are now known.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> A<sub>15</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
All Brauer tables of S<sub>15</sub> are now known
(contributed by Jürgen Müller).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> A<sub>16</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
All Brauer tables of S<sub>16</sub> are now known
(contributed by Jürgen Müller).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> A<sub>17</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
All Brauer tables except the 3-modular one of S<sub>17</sub>
are now known
(contributed by Jürgen Müller).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Co<sub>2</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The degree 156 538 character of Co<sub>2</sub> mod 2 is now
proved.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Co<sub>3</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
One more indicator of Co<sub>3</sub> mod 2 is now known.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> Fi<sub>22</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The faithful characters of 6.Fi<sub>22</sub> and 6.Fi<sub>22</sub>.2
mod 5
were corrected.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> L<sub>3</sub>(4)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The faithful characters of 12<sub>2</sub>.L<sub>3</sub>(4) mod 7 were
corrected.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> O<sub>8</sub><sup>+</sup>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The degree 50 596 characters of O<sub>8</sub><sup>+</sup>(3) mod 2
are now proved.
Consequently, also the degree 101 192 of O<sub>8</sub><sup>+</sup>(3).2<sub>1</sub> mod 2,
the degrees 50 596 and 101 192 of O<sub>8</sub><sup>+</sup>(3).2<sub>2</sub> mod 2,
the degrees 50 596 and 151 288 of O<sub>8</sub><sup>+</sup>(3).3 mod 2,
and the degree 202 384 of O<sub>8</sub><sup>+</sup>(3).4 mod 2 are now proved.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> ON</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of ON and ON.2 mod 19 were changed
in order to respect the choice of classes in Robert Wilson's
"Atlas of Group Representations".
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> ON</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of ON mod 11 and mod 31 are now known
(contributed by Markus Ottensmann),
as well as two new indicator values for ON mod 2.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> Ru</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of Ru and 2.Ru mod 5 and mod 7 were changed
in order to respect the choice of classes in Robert Wilson's
"Atlas of Group Representations".
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Ru</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of Ru and 2.Ru mod 13 and 29 are now known
(contributed by Frank Röhr),
as well as all indicator values of Ru mod 2.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> S<sub>6</sub>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The characters of S<sub>6</sub>(3) and 2.S<sub>6</sub>(3) mod 7 were
corrected;
these changes do not affect the tables of S<sub>6</sub>(3).2 and 2.S<sub>6</sub>(3).2
mod 7
(contributed by Jürgen Müller).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> Suz</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The faithful characters of 6.Suz and 6.Suz.2 mod 7 were
corrected
(contributed by Jürgen Müller).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Th</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of Th mod 19 is now known.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br /><br /><b>Ordinary Tables</b>
<div class="p"><!----></div>
The following changes affect several ordinary tables.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
Whitespace at the end of <tt>InfoText</tt> strings was removed.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
Various class fusions were added.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
Components <tt>tomidentifier</tt> and <tt>tomfusion</tt> were added
in order to provide a (preliminary) interface to
the library of tables of marks.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
In the library tables of alternating and symmetric groups,
the <tt>classtext</tt> components
(partitions parametrizing the conjugacy classes;
in some cases, this had been hidden inside the <tt>CAS</tt>
component of the table)
were replaced by values of the attribute <tt>ClassParameters</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The tables of L<sub>2</sub>(q) were added for those values of q for which
the table of marks of L<sub>2</sub>(q) is now contained in the <font face="helvetica"><font size="+0">GAP</font></font> library.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
In the library tables of symmetric groups,
the partitions parametrizing the irreducible characters
are stored on the tables,
as value of the attribute <tt>CharacterParameters</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The <tt>Identifier</tt> values of a few tables have been changed.
For example, the table of <tt>L4(3).2^2</tt> was previously known only as
<tt>psl(4,3).v4</tt>.
The old names are still valid.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The character tables with identifiers <tt>iu332</tt>, <tt>D2MJ4</tt>,
and <tt>P4L82</tt> were removed.
The former two tables were incomplete, the latter one was wrong.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The ordinary tables of all maximal subgroups
(and their class fusions)
are now available for the groups G<sub>2</sub>(3), J<sub>3</sub>.2, 2.M<sub>12</sub>,
M<sub>12</sub>.2, M<sub>22</sub>.2, and O<sub>8</sub><sup>+</sup>(3).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br />The following changes are assigned to specific simple groups,
and shown in alphabetical order.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> A<sub>6</sub></td><td valign="top"> : </td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table automorphisms of 4.A<sub>6</sub>.2<sub>3</sub> were corrected.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Fi<sub>22</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the maximal subgroup 2<sup>7</sup>:S<sub>6</sub>(2)
of Fi<sub>22</sub>.2 was added
(contributed by E. Mpono).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Fi<sub>22</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the maximal subgroup 2<sup>6</sup>:U<sub>4</sub>(2).2
of the maximal subgroup 2<sup>6</sup>:S<sub>6</sub>(2) of Fi<sub>22</sub> was added
(contributed by E. Mpono).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> HS</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables (and fusions) of several normalizers of chains of
p-subgroups were added.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> J<sub>4</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The classes and the characters of the maximal subgroup of type
2<sup>10</sup>:L<sub>5</sub>(2) were reordered,
and the identifier was changed from <tt>l52m10</tt> (from the <font face="helvetica"><font size="+0">CAS</font></font> library)
to <tt>2^10:L5(2)</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> McL</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the seventh maximal subgroup of McL.2 was added.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> O<sub>8</sub><sup>+</sup>(2)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The classes and the characters of the maximal subgroup of
type 2<sup>6</sup>:A<sub>8</sub> were reordered,
and the identifier was changed from <tt>mo81p</tt> (from the <font face="helvetica"><font size="+0">CAS</font></font> library) to
<tt>2^6:A8</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> O<sub>8</sub><sup>+</sup>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The fusions from O<sub>7</sub>(3) and 3<sup>6</sup>:L<sub>4</sub>(3) were changed
to the ones listed in the Atlas of Finite Groups.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> O<sub>10</sub><sup>+</sup>(2)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the maximal subgroup 2<sup>8</sup>:O<sub>8</sub><sup>+</sup>(2)
was added.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> S<sub>10</sub>(2)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the subgroup 2<sup>8</sup>:S<sub>8</sub>(2) was added.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> U<sub>4</sub>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of 2.U<sub>4</sub>(3).(2<sup>2</sup>)<sub>122</sub> and 6<sub>2</sub>.U<sub>4</sub>(3).2<sub>3</sub>′
were added.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br /><br /><b>Release of <font face="helvetica"><font size="+0">GAP</font></font> 4.2 in March 2000</b>
<div class="p"><!----></div>
<br /><br /><b>Brauer Tables</b>
<div class="p"><!----></div>
Changes are assigned to the simple group involved,
and shown in alphabetical order.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> A<sub>14</sub></td><td valign="top"> : </td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
Table of S<sub>14</sub> mod 2 is now known
(contributed by Dave Benson, added by Jürgen Müller).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> A<sub>16</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
Corrected principal block of the table of S<sub>16</sub> mod 2.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> ON</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of 3.ON mod 11 and 31 are now known.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> ON</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of 3.ON and 3.ON.2 mod 19 were changed
in order to respect the choice of classes in Robert Wilson's
"Atlas of Group Representations".
(This affects only the irreducibles of 3.ON of degrees 45090 and 77670.)
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br /><br /><b>Ordinary Tables</b>
<div class="p"><!----></div>
The following changes affect several ordinary tables.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
Various class fusions were added.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The <tt>galomorphisms</tt> components which had been contained in only a few
tables were removed.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The <tt>tomfusion</tt> values of L<sub>2</sub>(25) and 2<sup>5</sup>:S<sub>6</sub> were corrected.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
Element orders and power maps in the table with identifier
<tt>s61p</tt> were corrected.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The table with identifier <tt>2.cenc1</tt> was removed because it was
inconsistent.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
Two instances of the table of (A<sub>6</sub> ×A<sub>6</sub>):2<sup>2</sup> were unified.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The tables with identifiers <tt>J2.2M4</tt>, <tt>2^(2+4):(3x3):2^2</tt>,
and <tt>2^(2+4):(S3xS3)</tt> were unified;
the identifiers <tt>J2.2M5</tt> and <tt>2^(2+4):(S3xS3)</tt> can be used to
access the table.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The ordinary tables of all maximal subgroups
(and their class fusions)
are now available for the groups S<sub>6</sub>, J<sub>2</sub>.2, McL.2, Suz.2,
3.Suz, 3.Suz.2, Sz(32).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br />The following changes are assigned to specific simple groups,
and shown in alphabetical order.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> A<sub>6</sub></td><td valign="top"> : </td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of 12.A<sub>6</sub>.2<sub>3</sub> is now available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> Fi<sub>22</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The name of the table of the 7-th maximal subgroup
of Fi<sub>22</sub> was corrected from <tt>(2x2^(1+8):U4(2)):2</tt> to
<tt>(2x2^(1+8)):U4(2):2</tt>;
similarly, <tt>(2x2^(1+8):U4(2):2):2</tt> was corrected to
<tt>(2x2^(1+8)):(U4(2):2x2)</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Fi<sub>22</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of the maximal subgroups 2<sup>10</sup>:M<sub>22</sub>:2 of
Fi<sub>22</sub>.2 and 2<sup>11</sup>.M<sub>22</sub> of 2.Fi<sub>22</sub> are now available
via the names <tt>Fi22.2M4</tt> and <tt>2.Fi22M5</tt>, respectively.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> U<sub>3</sub>(5)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table with identifier <tt>U3(5).S3</tt> was removed;
it is replaced by the table with identifier <tt>U3(5).3.2</tt>
whose cosets of the outer automorphism group are ordered as in the
Atlas of Finite Groups.
The identifier <tt>U3(5).S3</tt> is now admissible for the table with
identifier <tt>U3(5).3.2</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> U<sub>4</sub>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table with identifier <tt>u4q3c</tt> was removed;
characters and power maps of this table were erroneous.
Apparently the table was thought to be that of 3<sub>2</sub>.U<sub>4</sub>(3).2<sub>3</sub><sup>′</sup>,
which can be accessed with the name <tt>3_2.U4(3).2_3'</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> U<sub>4</sub>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of 3<sub>2</sub>.U<sub>4</sub>(3).(2<sup>2</sup>)<sub>133</sub> and U<sub>4</sub>(3).(2<sup>2</sup>)<sub>133</sub>
are now available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br /><br /><b>Release of CTblLib 1.0 in January 2002</b>
<div class="p"><!----></div>
<br /><br /><b>Brauer Tables</b>
<div class="p"><!----></div>
Changes are assigned to the simple group involved,
and shown in alphabetical order.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> A<sub>14</sub></td><td valign="top"> : </td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of A<sub>14</sub> mod 3, 5, 7
and of S<sub>14</sub> mod 11, 13 are now known
(contributed by Jürgen Müller, using <font face="helvetica"><font size="+0">MOC</font></font> and the <font face="helvetica"><font size="+0">GAP</font></font> package
<tt>specht</tt>).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> A<sub>17</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of A<sub>17</sub> mod 3 is now known
(contributed by Jürgen Müller).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> F<sub>3+</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
All Brauer tables of the maximal subgroup 3<sup>7</sup>.O<sub>7</sub>(3),
and the 2-modular table of the maximal subgroup
(3 ×O<sub>8</sub><sup>+</sup>(3):3):2 are available
(contributed by Gerhard Hiß).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> L<sub>4</sub>(4)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of L<sub>4</sub>(4) mod 3, 5, 7, 17 are now known
(contributed by Gerhard Hiß).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Ly</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of Ly mod 37 and 67 are now known
(contributed by Jürgen Müller, Max Neunhöffer, Frank Röhr,
Robert Wilson).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> O<sub>8</sub><sup>+</sup>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of O<sub>8</sub><sup>+</sup>(3).S<sub>3</sub> mod 2 is available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> </td><td valign="top"> </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of O<sub>8</sub><sup>+</sup>(3).S<sub>3</sub> mod 2 is available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> S<sub>10</sub>(2)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of S<sub>10</sub>(2) mod 7, 11, 17, 31 are now known
(contributed by Gerhard Hiß).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br /><br /><b>Ordinary Tables</b>
<div class="p"><!----></div>
The following changes affect several ordinary tables.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The ordinary tables of the Schur covers of the symmetric groups
S<sub>14</sub>, S<sub>15</sub>, S<sub>16</sub>, S<sub>17</sub>, and S<sub>18</sub> are now available
(contributed by Gunter Malle).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The ordinary tables of all maximal subgroups
(and their class fusions)
are now available for the group 2.HS
(contributed by Ulrike Muthmann, Markus Ottensmann, and Frank Röhr).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The ordinary tables of all maximal subgroups
(and their class fusions)
are now available for the groups 2.Suz and 6.Suz
(contributed by Thomas Breuer and Frank Himstedt).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The ordinary tables of all maximal subgroups (and their class fusions)
are now available for the group S<sub>6</sub>(3).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br />The following changes are assigned to specific simple groups,
and shown in alphabetical order.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> E<sub>6</sub>(2)</td><td valign="top"> : </td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the Chevalley group E<sub>6</sub>(2) is now available
(contributed by B. Fischer).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> F<sub>3+</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the maximal subgroup
2<sup>1+12</sup>.3<sub>1</sub>.U<sub>4</sub>(3).2<sub>2</sub><sup>′</sup> of F<sub>3+</sub> is now available
via the names <tt>2^(1+12).3_1.U4(3).2_2'</tt>, <tt>F3+M9</tt>,
and <tt>F3+C2B</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b></b></td><td valign="top"> </td><td valign="top"> </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the maximal subgroup
3<sup>3</sup>.[3<sup>10</sup>].GL3(3) of F<sub>3+</sub> is now available
via the name <tt>3^3.[3^10].GL3(3)</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> F<sub>3+</sub>.2</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the maximal subgroup
3<sup>7</sup>.O<sub>7</sub>(3):2 of F<sub>3+</sub>.2 is now available
(contributed by Faryad Ali).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> HS</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The earlier (since <font face="helvetica"><font size="+0">CAS</font></font> times) stored fusion of
2 ×A<sub>6</sub>.2<sup>2</sup> into HS did not lift to 2.HS
and therefore was replaced by a compatible map.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> L<sub>3</sub>(4)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of 2<sup>2</sup>.L<sub>3</sub>(4).2<sub>2</sub> is now available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> L<sub>4</sub>(9)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of L<sub>4</sub>(9) is now available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> M</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the maximal subgroup 2<sup>1+24</sup>.Co<sub>1</sub> is now available
(contributed by Simon Norton).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> S<sub>4</sub>(7)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of S<sub>4</sub>(7) and S<sub>4</sub>(7).2 are now available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> S<sub>6</sub>(2)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the maximal subgroup 2<sup>6</sup>:S<sub>8</sub>
of 2<sup>6</sup>:S<sub>6</sub>(2) (which is maximal in Fi<sub>22</sub>) is now available
(contributed by Faryad Ali).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> S<sub>6</sub>(5)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of S<sub>6</sub>(4) is now available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> S<sub>6</sub>(5)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of S<sub>6</sub>(5) is now available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> S<sub>12</sub>(2)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of S<sub>12</sub>(2) is now available
(contributed by Christoph Köhler).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> Suz</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The earlier (since <font face="helvetica"><font size="+0">CAS</font></font> times) stored fusion of
(3<sup>2</sup> :4 ×A<sub>6</sub>).2 into Suz did not lift to 3.Suz
and therefore was replaced by a compatible map.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> U<sub>4</sub>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of 3<sub>1</sub>.U<sub>4</sub>(3).2<sub>2</sub><sup>′</sup> was added.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> U<sub>4</sub>(4)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of U<sub>4</sub>(4) is now available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> U<sub>6</sub>(2)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the Schur cover (2<sup>2</sup> ×3).U<sub>6</sub>(2)
is now available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br /><br /><b>Release of CTblLib 1.1 in February 2004</b>
<div class="p"><!----></div>
<br /><br /><b>Brauer Tables</b>
<div class="p"><!----></div>
The following changes affect several Brauer tables.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The p-modular tables of G.S<sub>3</sub> are available for all prime divisors
p of |G|, for G one of L<sub>3</sub>(7), 3.L<sub>3</sub>(7), U<sub>3</sub>(5), 3.U<sub>3</sub>(5),
U<sub>3</sub>(8), 3.U<sub>3</sub>(8), U<sub>3</sub>(11), and 3.U<sub>3</sub>(11).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
The following changes are assigned to the simple group involved,
and shown in alphabetical order.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Co<sub>2</sub></td><td valign="top"> : </td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The indicators of the 36938 and 83948 in Co<sub>2</sub> mod 2 are +
(contributed by Jon Thackray).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Co<sub>3</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The indicator of the 88000 in Co<sub>3</sub> mod 2 is +
(contributed by Jon Thackray).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> J<sub>4</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of J<sub>4</sub>M1 mod 3 and 11 are available
(contributed by Christoph Jansen).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> O<sub>8</sub><sup>+</sup>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of O<sub>8</sub><sup>+</sup>(3).S<sub>4</sub> mod 2, 5, and 7 are
available
(contributed by Christoph Jansen).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> ON</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of ON.2 and 3.ON.2 mod 11 and 31 are available
(contributed by Jürgen Müller).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> ON</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The indicator of the 25916 in ON mod 2 is +
(contributed by Jon Thackray).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Suz</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The indicators of 10504 in Suz mod 2 and Suz.2 mod 2
are +
(contributed by Jon Thackray).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br /><br /><b>Ordinary Tables</b>
<div class="p"><!----></div>
The following changes affect several ordinary tables.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The table automorphisms were corrected for the tables with the identifiers
<tt>A17</tt>, <tt>2.A4xS3</tt>, <tt>4.M22M6</tt>, <tt>3.2^(2+4):(3x3):2</tt>,
<tt>3^(1+6):2^(3+4):3^2:2</tt>, <tt>5:4x2.A5</tt>, <tt>D8xV4</tt>,
<tt>3.3^5.U4(2)</tt>, <tt>3^5.U4(2)</tt>, <tt>group3</tt>, <tt>s61p</tt>,
<tt>2.(A4xA4)</tt>, <tt>3^3:A4</tt>, <tt>3^7.O7(3)</tt>, <tt>ThN2</tt>, and
<tt>2^2.2E6(2).2</tt>;
one reason for these errors were missing power maps.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The formerly admissible names <tt>c1</tt>, <tt>c2</tt>, <tt>c3</tt> for the groups
Co<sub>1</sub>, Co<sub>2</sub>, Co<sub>3</sub> have been removed, because these names are now
admissible names of cyclic groups.
The names <tt>c1m1</tt>, <tt>c1m4</tt>, <tt>c1m5</tt>, <tt>c1m24</tt>,
<tt>c1n3</tt>, <tt>c2m1</tt>, <tt>c2m2</tt>, <tt>c2m3</tt>, <tt>c2m4</tt>, <tt>c2m5</tt>,
<tt>c2m6</tt>, <tt>c2m7</tt>, <tt>c2m8</tt>, <tt>c2m9</tt>, <tt>c2m10</tt>, <tt>c2m11</tt>,
<tt>c2m22</tt>, (now called <tt>M22C2A</tt>), <tt>c2m24</tt> (now called <tt>M24C2B</tt>),
<tt>c3m1</tt>, <tt>c3m2</tt>, <tt>c3m3</tt>, <tt>c3m4</tt>,
<tt>c3m5</tt>, <tt>c3m6</tt>, <tt>c3m7</tt>, <tt>c3m8</tt>, <tt>c3m9</tt>, <tt>c3m10</tt>,
<tt>c3m11</tt>, <tt>c3m12</tt>, <tt>c3m13</tt>, <tt>c3m14</tt>, <tt>c3n2</tt>, <tt>c3n3</tt>,
<tt>c3n5</tt>, <tt>mcn2</tt>, <tt>mcn3</tt>, <tt>mcn5</tt>, <tt>om83</tt>, <tt>o8m2</tt>,
<tt>o8m2.2</tt>, <tt>o10m2</tt>, <tt>o10m2c</tt>, <tt>o12m2</tt>, <tt>rvn2</tt>,
<tt>s2m11</tt>, <tt>s2m12</tt>,
<tt>s2m21</tt>, <tt>s2m23</tt>, and <tt>s2m24</tt> (now called <tt>M24C2A</tt>)
were removed because they would refer to maximal subgroups of other groups
or of groups with nonadmissible names.
The names <tt>u4q3.s3</tt> and <tt>f22u3</tt> were removed, the table is now
available with the name <tt>S3xU4(3)</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The ordering of maximal subgroups was changed for A<sub>5</sub>.2, A<sub>6</sub>.2<sub>1</sub>,
J<sub>3</sub>.2, M<sub>12</sub>.2, and McL.2, in order to be compatible with the
<font face="helvetica"><font size="+0">ATLAS</font></font> of Group Representations.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The following class fusions were corrected.
2<sup>7</sup>:S<sub>6</sub>(2) onto S<sub>6</sub>(2) and into Fi<sub>22</sub>.2;
3.3<sup>1+4</sup>:4S<sub>5</sub> into 3.McL.2;
D<sub>8</sub> ×V<sub>4</sub> into HS;
3.2<sup>2+4</sup>:(3 ×3):2 into 3.McL, 3.2<sup>4</sup>:A<sub>7</sub>,
and 3.McLM10;
4.M<sub>22</sub>M6 into 4.M<sub>22</sub>;
G<sub>2</sub>(3)M6 into G<sub>2</sub>(3);
A<sub>5</sub>.2 into M<sub>12</sub>.2;
A<sub>11</sub>Syl2 into A<sub>11</sub>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
Missing power maps were added for the tables
<tt>suzs2</tt>, <tt>Fi22N3</tt>, <tt>RuN2</tt>, <tt>SuzN2</tt>, <tt>ThN2</tt>,
for L<sub>2</sub>(q), for various values of q,
and for <tt>7:3</tt>, <tt>23:11</tt>, <tt>11:10</tt>,
due to the availability of power maps in the underlying generic character
tables.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The tables of all maximal subgroups are available for
A<sub>5</sub>, A<sub>6</sub>, A<sub>7</sub>, A<sub>7</sub>.2, G<sub>2</sub>(4), L<sub>2</sub>(11), L<sub>2</sub>(11).2, U<sub>3</sub>(3).2,
U<sub>5</sub>(2).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
Several ordinary tables were added for which the tables of marks of the
underlying groups are available in the <font face="helvetica"><font size="+0">GAP</font></font> Library of Tables of Marks;
this includes direct products and tables of small groups that can be computed
easily with standard methods.
The other way round, each ordinary table in the library for which the table
of marks is contained in the <font face="helvetica"><font size="+0">GAP</font></font> Library of Tables of Marks stores a
class fusion into the table of marks.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
Several ordinary tables of Sylow normalizers in sporadic simple
groups are available, including the normalizers of cyclic Sylow subgroups.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The ordinary tables of G.S<sub>3</sub> are available for G one of
2<sup>2</sup>.L<sub>3</sub>(4), L<sub>3</sub>(7), 3.L<sub>3</sub>(7), 2<sup>2</sup>.O<sub>8</sub><sup>+</sup>(2), 3.U<sub>3</sub>(5), U<sub>3</sub>(8),
3.U<sub>3</sub>(8), U<sub>3</sub>(11), 3.U<sub>3</sub>(11).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
The ordinary tables of L<sub>4</sub>(5), O<sub>7</sub>(5), O<sub>7</sub>(5).2, O<sub>9</sub>(3), S<sub>4</sub>(8),
S<sub>8</sub>(3), U<sub>4</sub>(5) are available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="716">
Generic character tables are available for the double covers of
alternating and symmetric groups
(contributed by Felix Noeske).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br />The following changes are assigned to specific simple groups,
and shown in alphabetical order.
<div class="p"><!----></div>
<br />
<table>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> A<sub>6</sub></td><td valign="top"> : </td><td valign="top">
<td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The fusions of A<sub>6</sub>, A<sub>6</sub>.2<sub>1</sub>, 2.A<sub>6</sub> into the tables of marks
were changed in order to make diagrams of fusions commutative.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> B</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of the maximal subgroups of the types
3<sup>1+8</sup>.2<sup>1+6</sup>.U<sub>4</sub>(2).2 and (2<sup>2</sup> ×F<sub>4</sub>(2)):2,
and the table of the Sylow 7 normalizer are available,
as well as the table of the maximal subgroup of the type
(S<sub>3</sub> ×2.Fi<sub>22</sub>).2 in 2.B.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Co<sub>1</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the Sylow 5 normalizer is available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Co<sub>2</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the Sylow 2, 3, and 7 normalizers are available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> Fi<sub>24</sub><sup>′</sup></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of the maximal subgroups
3<sup>2</sup>.3<sup>4</sup>.3<sup>8</sup>.(A<sub>5</sub> ×2A<sub>4</sub>).2, 2<sup>3+12</sup>.(L<sub>3</sub>(2) ×A<sub>6</sub>), and
2<sup>6+8</sup>.(S<sub>3</sub> ×A<sub>8</sub>) and their class fusions are now available
(contributed by Alexander Hulpke).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> </td><td valign="top"> </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of the Sylow 5 and 7 normalizer are available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> HN</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the maximal subgroup 4.HS.2 of HN.2 is available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> HS</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of HS into Co<sub>3</sub> was replaced by one
that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> J<sub>2</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of 2.J<sub>2</sub>.2 into 2.Suz was replaced by one
that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> </td><td valign="top"> </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of 2.HS.2 into HN was corrected.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> J<sub>4</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table with identifier <tt>(3^(1+2)x2).SD16</tt> is <b>not</b>
that of the Sylow 3 normalizer in J<sub>4</sub>; the name <tt>J4N3</tt> is no longer
admissible for this table (reported by G. Navarro and A. Moreto).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> </td><td valign="top"> </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the Sylow 3 normalizer in J<sub>4</sub> is available,
via the names <tt>(2x3^(1+2)_+:8):2</tt> and <tt>J4N3</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> L<sub>2</sub>(11)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of L<sub>2</sub>(11) into J<sub>1</sub> was replaced by one
that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> L<sub>2</sub>(16)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusions of L<sub>2</sub>(16).2 into J<sub>3</sub> and of L<sub>2</sub>(16).4
into J<sub>3</sub>.2 were replaced by maps
that are compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> L<sub>2</sub>(19)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of L<sub>2</sub>(19) into J<sub>3</sub> was replaced by
one that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> L<sub>2</sub>(27)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of L<sub>2</sub>(27).3 into S<sub>6</sub>(3) was replaced by
one that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> L<sub>3</sub>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusions of L<sub>3</sub>(3).2 into G<sub>2</sub>(3)
and S<sub>6</sub>(3) were replaced by
maps that are compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> L<sub>3</sub>(4)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusions of 4<sub>2</sub>.L<sub>3</sub>(4).2<sub>1</sub> into ON
and of 4<sub>2</sub>.L<sub>3</sub>(4).2<sub>3</sub> into 4.U<sub>4</sub>(3).2<sub>3</sub> were replaced by
maps that are compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> </td><td valign="top"> </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of 2<sup>2</sup>.L<sub>3</sub>(4).2<sub>3</sub> and 2<sup>2</sup>.L<sub>3</sub>(4).3 are available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> L<sub>3</sub>(11)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of L<sub>3</sub>(11) is available
(contributed by Frank Lübeck,
computed with a program written by Boris Hemkemeier and Ulf Jürgens).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> L<sub>4</sub>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of L<sub>4</sub>(3).2<sub>2</sub> into O<sub>7</sub>(3) was replaced by
one that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> L<sub>8</sub>(2)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of L<sub>8</sub>(2) is available
(contributed by Frank Lübeck,
computed with a program written by Boris Hemkemeier and Ulf Jürgens).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> M</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of the Sylow 11 and 13 normalizer in M are available,
via the names <tt>MN11</tt> and <tt>MN13</tt>.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> </td><td valign="top"> </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables with the names <tt>4.2^2</tt>, <tt>(2^2x3).2</tt>,
<tt>1/2(8xS3)</tt>, <tt>M12C4</tt>, <tt>7^1+2.6</tt>, <tt>2x3.A6</tt>,
<tt>5^1+2.2A4</tt>, <tt>(4xA6).2^2</tt>, <tt>13^1+2.2A4</tt>,
<tt>7^1+4.2A7</tt> are available
(contributed by Simon Norton).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> M<sub>23</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of M<sub>23</sub> into Co<sub>3</sub> was replaced by
one that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> M<sub>24</sub></td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of 2<sup>4</sup>:A<sub>8</sub> into M<sub>24</sub> was replaced by
one that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> McL</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of McL.2 into Co<sub>3</sub> was replaced by one
that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>***</b></td><td valign="top"> </td><td valign="top"> </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The 2nd power map of the table of the maximal subgroup of type
3.3<sup>1+4</sup>:4S<sub>5</sub> of 3.McL.2 was corrected.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> O<sub>8</sub><sup>−</sup>(2)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of O<sub>8</sub><sup>−</sup>(2).2 into S<sub>8</sub>(2) was replaced
by one that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> O<sub>8</sub><sup>+</sup>(2)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of 2<sup>2</sup>.O<sub>8</sub><sup>+</sup>(2).2 and 2<sup>2</sup>.O<sub>8</sub><sup>+</sup>(2).3
are available, as well as the table of the maximal subgroup of the type
2<sup>1+6</sup><sub>+</sub>.A<sub>8</sub> of 2.O<sub>8</sub><sup>+</sup>(2).
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> O<sub>8</sub><sup>+</sup>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of O<sub>8</sub><sup>+</sup>(3).D<sub>8</sub> is available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> </td><td valign="top"> </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The tables of the maximal subgroup 2<sup>2</sup>.(U<sub>3</sub>(3).2 ×S<sub>4</sub>)
of O<sub>8</sub><sup>+</sup>(3).S<sub>4</sub> and of the maximal subgroups
3<sup>3+6</sup>:(L<sub>3</sub>(3) ×D<sub>8</sub>) and 3<sup>6</sup>.L<sub>4</sub>(3).D<sub>8</sub> of O<sub>8</sub><sup>+</sup>(3).D<sub>8</sub>
are available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> O<sub>8</sub><sup>−</sup>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of O<sub>8</sub><sup>−</sup>(3).2<sub>1</sub> is available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NeW</b></td><td valign="top"> O<sub>9</sub>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of the maximal subgroup of type 2<sup>8</sup>.A<sub>9</sub>
is available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> S<sub>4</sub>(4)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of S<sub>4</sub>(4).2 into S<sub>8</sub>(2) was replaced by one
that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> S<sub>6</sub>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of 3<sup>6</sup>:L<sub>3</sub>(3) into S<sub>6</sub>(3) was replaced
by one that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>C</b></td><td valign="top"> U<sub>3</sub>(5)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The class fusion of 3.U<sub>3</sub>(5) into 3.McL was replaced by one
that is compatible with the Brauer tables available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr>
<tr><td valign="top" align="right"><b>NEW</b></td><td valign="top"> U<sub>4</sub>(3)</td><td valign="top"> : </td><td valign="top">
</td><td valign="top"><table border="0"><tr><td valign="top"></td><td width="633">
The table of 2<sup>2</sup>.U4(3).(2<sup>2</sup>)<sub>122</sub> is available.
</td></tr></table><!--vbox-->
</td><td valign="top"></td></tr></td></tr></table><!--hboxt--></table>
<div class="p"><!----></div>
<br /><br />
<div class="p"><!----></div>
Last update November 12th, 2003.
<div class="p"><!----></div>
<div class="p"><!----></div>
<br /><br /><hr /><small>File translated from
T<sub><font size="-1">E</font></sub>X
by <a href="http://hutchinson.belmont.ma.us/tth/">
T<sub><font size="-1">T</font></sub>H</a>,
version 3.55.<br />On 31 Mar 2004, 10:54.</small>
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