|
10 | 10 | } |
11 | 11 | </style> |
12 | 12 |
|
13 | | -<p> {{ place_code('gg') }}</p> |
14 | | - <p><h2>{{ KNOWL('gg.group_action_invariants', title='Group action invariants') }}</h2> |
| 13 | +<p> {{ place_code('gg') }}</p> |
| 14 | + |
| 15 | +<h2> {{ KNOWL('gg.invariants', title='Group invariants') }}</h2> |
| 16 | + <div> |
15 | 17 | <table> |
16 | | - <tr><td>{{KNOWL('gg.degree', 'Degree')}} $n$:<td> <td>${{info.n}}$</td> |
17 | | - <td>{{ place_code('n') }}</td></tr> |
| 18 | + <tr><td>{{KNOWL('group.small_group_label','Abstract group')}}:</td><td> </td><td>{{info.groupid | safe}}</td> |
| 19 | + <td>{{place_code('id')}}</td></tr> |
| 20 | + <tr><td>{{KNOWL('group.order','Order')}}:</td><td> </td><td>{{info.ordermsg }}</td> |
| 21 | + <td>{{place_code('order')}}</td></tr> |
| 22 | + <tr><td>{{KNOWL('group.cyclic','Cyclic')}}:</td><td> </td><td>{{info.yesno(info.cyc)}}</td> |
| 23 | + <td>{{place_code('cyclic')}}</td></tr> |
| 24 | + <tr><td>{{KNOWL('group.abelian', 'Abelian')}}:</td><td> </td><td>{{info.yesno(info.ab)}}</td> |
| 25 | + <td>{{place_code('abelian')}}</td></tr> |
| 26 | + <tr><td>{{KNOWL('group.solvable', 'Solvable')}}:</td><td> </td><td>{{info.yesno(info.solv)}}</td> |
| 27 | + <td>{{place_code('solvable')}}</td></tr> |
| 28 | + <tr><td class="nowrap">{{KNOWL('group.nilpotent', 'Nilpotency class')}}:</td><td> </td><td>{{info.nilpotency}}</td><td>{{ place_code('nilpotent') }}</td></tr> |
| 29 | + </table> |
| 30 | + </div> |
| 31 | + |
| 32 | + <h2>{{ KNOWL('gg.group_action_invariants', title='Group action invariants') }}</h2> |
| 33 | + <table> |
| 34 | + <tr><td>{{KNOWL('gg.degree', 'Degree')}} $n$:</td><td> </td><td>${{info.n}}$</td> |
| 35 | + <td>{{ place_code('n') }}</td></tr> |
18 | 36 | <tr><td class="nowrap">{{KNOWL('gg.tnumber', 'Transitive number')}} $t$:<td> <td>${{info.t}}$</td> |
19 | | - <td>{{ place_code('t') }}</td></tr> |
20 | | - {% if info.pretty_name %} |
21 | | - <tr><td>{{KNOWL('gg.simple_name', title='Group')}}:<td> <td>{{info.pretty_name}}</tr> |
22 | | - {% endif %} |
| 37 | + <td>{{ place_code('t') }}</td></tr> |
23 | 38 | {% if info.n < 16 %} |
24 | | - <tr><td>{{KNOWL('gg.conway_name', title='CHM label')}}:<td> <td> |
| 39 | + <tr><td>{{KNOWL('gg.conway_name', title='CHM label')}}:</td><td> </td><td> |
25 | 40 | {% if info.n == 1 %} |
26 | 41 | {{info.name}} |
27 | 42 | {% else %} |
28 | 43 | ${{info.name}}$ |
29 | 44 | {% endif %} |
30 | | - </tr> |
| 45 | + </td></tr> |
31 | 46 | {% endif %} |
32 | | - <tr><td>{{KNOWL('gg.parity','Parity')}}:<td> <td>{{info.parity}} |
| 47 | + <tr><td>{{KNOWL('gg.parity','Parity')}}:</td><td> </td><td>{{info.parity}}</td> |
33 | 48 | <td>{{ place_code('even') }}</td></tr> |
34 | | - <tr><td>{{KNOWL('gg.primitive', 'Primitive')}}:<td> <td>{{info.yesno(info.prim)}}</td> |
| 49 | + <tr><td>{{KNOWL('gg.primitive', 'Primitive')}}:</td><td> </td><td>{{info.yesno(info.prim)}}</td> |
35 | 50 | <td>{{ place_code('primitive') }}</td></tr> |
36 | | - <td>{{ place_code('nilpotent') }}</td></tr> |
37 | | - <tr><td class="nowrap">{{KNOWL('gg.field_automorphisms', '$\card{\Aut(F/K)}$')}}:<td> <td>${{info.auts}}$</td> |
| 51 | + <tr><td class="nowrap">{{KNOWL('gg.field_automorphisms', '$\card{\Aut(F/K)}$')}}:</td><td> </td><td>${{info.auts}}$</td> |
38 | 52 | <td>{{ place_code('auts') }}</td></tr> |
39 | | - <tr><td>{{KNOWL('group.generators', 'Generators')}}:<td> <td>{{info.gens}} |
| 53 | + <tr><td>{{KNOWL('group.generators', 'Generators')}}:</td><td> </td><td>{{info.gens}}</td> |
40 | 54 | <td>{{ place_code('gens') }}</td></tr> |
41 | 55 | </table> |
42 | | - </p> |
43 | 56 |
|
44 | | - <p><h2>{{KNOWL('gg.resolvents', 'Low degree resolvents')}}</h2> |
| 57 | + <h2>{{KNOWL('gg.resolvents', 'Low degree resolvents')}}</h2> |
45 | 58 | <blockquote> |
46 | 59 | {{info.resolve|safe}} |
47 | 60 |
|
48 | | -<p> Resolvents shown for degrees $\leq {{info.wgg.quotient_bound()}}$ |
| 61 | + <p>Resolvents shown for degrees $\leq {{info.wgg.quotient_bound()}}$</p> |
49 | 62 | </blockquote> |
50 | 63 |
|
51 | | - <p><h2>{{ KNOWL('gg.subfields', title='Subfields') }}</h2> |
52 | | - <p> |
| 64 | + <h2>{{ KNOWL('gg.subfields', title='Subfields') }}</h2> |
53 | 65 | <blockquote> |
54 | 66 | {{info.subinfo|safe}} |
55 | 67 | </blockquote> |
56 | | - </p> |
57 | 68 |
|
58 | | - <p><h2>{{ KNOWL('gg.other_representations', title='Low degree siblings') }}</h2> |
59 | | - <p> |
| 69 | + <h2>{{ KNOWL('gg.other_representations', title='Low degree siblings') }}</h2> |
60 | 70 | <blockquote> |
61 | 71 | {{info.otherreps|safe}} |
62 | 72 | </blockquote> |
63 | 73 | <blockquote> |
64 | 74 | {{info.arith_equiv|safe}} |
65 | 75 | </blockquote> |
66 | | - </p> |
67 | 76 |
|
68 | | - <p><h2>{{ KNOWL('gg.conjugacy_classes', title='Conjugacy classes') }}</h2> |
69 | | - <p> |
| 77 | + <h2>{{ KNOWL('gg.conjugacy_classes', title='Conjugacy classes') }}</h2> |
70 | 78 |
|
71 | 79 | {% if info.cclasses is defined %} |
72 | 80 | <table class="ntdata"> |
|
85 | 93 | </tbody> |
86 | 94 | </table> |
87 | 95 | <p> |
88 | | - {{KNOWL('gg.malle_a', "Malle's constant $a(G)$")}}: |
| 96 | + {{KNOWL('gg.malle_a', "Malle's constant $a(G)$")}}: |
89 | 97 | {% if info.malle_a is not none %} |
90 | | - ${{info.malle_a}}$ |
| 98 | + ${{info.malle_a}}$ |
91 | 99 | {% else %} |
92 | 100 | not computed |
93 | 101 | {% endif %} |
|
99 | 107 | </p> |
100 | 108 | <p>{{ place_code('ccs') }}</p> |
101 | 109 |
|
102 | | - |
103 | | - |
104 | | -<p><h2> {{ KNOWL('gg.invariants', title='Group invariants') }}</h2> |
105 | | - <div> |
106 | | - <table> |
107 | | - <tr><td>{{KNOWL('group.order','Order')}}:<td> <td>{{info.ordermsg }}</td> |
108 | | - <td>{{place_code('order')}}</td></tr> |
109 | | - <tr><td>{{KNOWL('group.cyclic','Cyclic')}}:<td> <td>{{info.yesno(info.cyc)}}</td> |
110 | | - <td>{{place_code('cyclic')}}</td></tr> |
111 | | - <tr><td>{{KNOWL('group.abelian', 'Abelian')}}:<td> <td>{{info.yesno(info.ab)}}</td> |
112 | | - <td>{{place_code('abelian')}}</td></tr> |
113 | | - <tr><td>{{KNOWL('group.solvable', 'Solvable')}}:<td> <td>{{info.yesno(info.solv)}}</td> |
114 | | - <td>{{place_code('solvable')}}</td></tr> |
115 | | - <tr><td class="nowrap">{{KNOWL('group.nilpotent', 'Nilpotency class')}}:<td> <td>{{info.nilpotency}}</td> |
116 | | - <tr><td>{{KNOWL('group.small_group_label','Label')}}:<td> <td>{{info.groupid | safe}} |
117 | | - <td>{{place_code('id')}}</td></tr> |
118 | | - <tr><td>{{KNOWL('group.complex_character_table', 'Character table')}}: |
| 110 | + <h2>{{KNOWL('group.complex_character_table', 'Character table')}}</h2> |
119 | 111 | {% if not info.wgg.can_chartable %} |
120 | | - <td> |
121 | | - <td> not computed |
122 | | - </table> </div> </p> |
| 112 | + <p>Character table not computed</p> |
123 | 113 | {% elif info.chartable %} |
124 | | - </table> |
125 | | - </div> |
126 | | - </p> |
127 | | - <p> |
128 | | - {% include 'character-table.html' %} |
| 114 | + {% include 'character-table.html' %} |
129 | 115 | {% else %} |
130 | | - <td> |
131 | | - <td> |
132 | | - {{ info.chartable_knowl | safe }} |
133 | | - </table> </div> </p> |
| 116 | + {{ info.chartable_knowl | safe }} |
134 | 117 | {% endif %} |
135 | 118 |
|
136 | 119 | <p>{{place_code('char_table')}}</p> |
137 | 120 |
|
| 121 | + |
138 | 122 | {% if info.int_reps %} |
139 | | -<p><h2>{{ KNOWL('gg.int_modules', title='Indecomposable integral representations') }}</h2> |
140 | | -</p> |
| 123 | +<h2>{{ KNOWL('gg.int_modules', title='Indecomposable integral representations') }}</h2> |
141 | 124 | <table> |
142 | | -<tr><td> |
| 125 | +<tr><td> |
143 | 126 | {% if info['int_reps_complete'] > 0 %} |
144 | | -Complete |
| 127 | +Complete |
145 | 128 | {% else %} |
146 | 129 | Partial |
147 | 130 | {% endif %} |
148 | 131 | list of indecomposable integral representations: |
149 | 132 | <p> |
150 | 133 | <div> |
151 | 134 | <table class="ntdata reptable"> |
152 | | - <tr><th>{{ KNOWL('gg.int_modules.names', title='Name') }}</th> <th>Dim</th> |
| 135 | + <tr><th>{{ KNOWL('gg.int_modules.names', title='Name') }}</th> <th>Dim</th> |
153 | 136 | {% for gen in info['int_rep_classes'] %} |
154 | 137 | <th> ${{ gen | safe }} \mapsto $ </th> |
155 | 138 | {% endfor %} |
156 | 139 | </tr> |
157 | 140 | {% for rep in info['int_reps'] %} |
158 | 141 | <tr> |
159 | | - <td> {{ rep['name'] | safe }} </td> <td> ${{rep['dim'] }}$ </td> |
| 142 | + <td> {{ rep['name'] | safe }} </td> <td> ${{rep['dim'] }}$ </td> |
160 | 143 | {% for gen in rep['gens'] %} |
161 | 144 | <td> ${{ gen | safe }}$ </td> |
162 | 145 | {% endfor %} |
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