Projective Planes of Order 49 Related to t109

I am currently compiling a list of known projective planes of order 49. As part of this enumeration, here are listed the plane t109 and all known planes of order 49 obtained from it by dualizing and deriving. Coming soon: also planes related by the method of lifting quotients. This list is currently incomplete; check back later for a complete enumeration.

Following the table is a key to the table.

Known Projective Planes of Order 49 Related to t109

Entry	Plane	\|Autgp\|	Point Orbits	Line Orbits	7-rank
1	Translation Plane t109, dual dt109	28812	1⁶,2²²,2401	1,49⁶,98²²	941
2	t109_0_0, dt109_0_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
3	t109_0_1, dt109_0_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
4	t109_0_2, dt109_0_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
5	t109_0_3, dt109_0_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
6	t109_0_4, dt109_0_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
7	t109_0_5, dt109_0_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
8	t109_0_6, dt109_0_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
9	t109_0_7, dt109_0_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
10	t109_1_0, dt109_1_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
11	t109_1_1, dt109_1_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
12	t109_1_2, dt109_1_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
13	t109_1_3, dt109_1_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
14	t109_1_4, dt109_1_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
15	t109_1_5, dt109_1_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
16	t109_1_6, dt109_1_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
17	t109_1_7, dt109_1_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
18	t109_2_0, dt109_2_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
19	t109_2_1, dt109_2_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
20	t109_2_2, dt109_2_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
21	t109_2_3, dt109_2_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
22	t109_2_4, dt109_2_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
23	t109_2_5, dt109_2_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
24	t109_2_6, dt109_2_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
25	t109_2_7, dt109_2_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
26	t109_3_0, dt109_3_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
27	t109_3_1, dt109_3_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
28	t109_3_2, dt109_3_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
29	t109_3_3, dt109_3_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
30	t109_3_4, dt109_3_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
31	t109_3_5, dt109_3_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
32	t109_3_6, dt109_3_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
33	t109_3_7, dt109_3_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
34	t109_4_0, dt109_4_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
35	t109_4_1, dt109_4_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
36	t109_4_2, dt109_4_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
37	t109_4_3, dt109_4_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
38	t109_4_4, dt109_4_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
39	t109_4_5, dt109_4_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
40	t109_4_6, dt109_4_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
41	t109_4_7, dt109_4_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
42	t109_5_0, dt109_5_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
43	t109_5_1, dt109_5_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
44	t109_5_2, dt109_5_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
45	t109_5_3, dt109_5_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
46	t109_5_4, dt109_5_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
47	t109_5_5, dt109_5_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
48	t109_5_6, dt109_5_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
49	t109_5_7, dt109_5_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
50	t109_6_0, dt109_6_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
51	t109_6_1, dt109_6_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
52	t109_6_2, dt109_6_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
53	t109_6_3, dt109_6_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
54	t109_6_4, dt109_6_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
55	t109_6_5, dt109_6_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
56	t109_6_6, dt109_6_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
57	t109_6_7, dt109_6_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
58	t109_7_0, dt109_7_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
59	t109_7_1, dt109_7_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
60	t109_7_2, dt109_7_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
61	t109_7_3, dt109_7_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
62	t109_7_4, dt109_7_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
63	t109_7_5, dt109_7_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
64	t109_7_6, dt109_7_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
65	t109_7_7, dt109_7_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
66	t109_8_0, dt109_8_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
67	t109_8_1, dt109_8_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
68	t109_8_2, dt109_8_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
69	t109_8_3, dt109_8_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
70	t109_8_4, dt109_8_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
71	t109_8_5, dt109_8_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
72	t109_8_6, dt109_8_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
73	t109_8_7, dt109_8_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
74	t109_9_0, dt109_9_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
75	t109_9_1, dt109_9_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
76	t109_9_2, dt109_9_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
77	t109_9_3, dt109_9_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
78	t109_9_4, dt109_9_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
79	t109_9_5, dt109_9_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
80	t109_9_6, dt109_9_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
81	t109_9_7, dt109_9_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
82	t109_10_0, dt109_10_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
83	t109_10_1, dt109_10_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
84	t109_10_2, dt109_10_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
85	t109_10_3, dt109_10_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
86	t109_10_4, dt109_10_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
87	t109_10_5, dt109_10_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
88	t109_10_6, dt109_10_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
89	t109_10_7, dt109_10_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
90	t109_11_0, dt109_11_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
91	t109_11_1, dt109_11_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
92	t109_11_2, dt109_11_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
93	t109_11_3, dt109_11_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
94	t109_11_4, dt109_11_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
95	t109_11_5, dt109_11_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
96	t109_11_6, dt109_11_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
97	t109_11_7, dt109_11_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
98	t109_12_0, dt109_12_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
99	t109_12_1, dt109_12_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
100	t109_12_2, dt109_12_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
101	t109_12_3, dt109_12_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
102	t109_12_4, dt109_12_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
103	t109_12_5, dt109_12_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
104	t109_12_6, dt109_12_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
105	t109_12_7, dt109_12_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
106	t109_13_0, dt109_13_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
107	t109_13_1, dt109_13_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
108	t109_13_2, dt109_13_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
109	t109_13_3, dt109_13_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
110	t109_13_4, dt109_13_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
111	t109_13_5, dt109_13_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
112	t109_13_6, dt109_13_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
113	t109_13_7, dt109_13_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
114	t109_14_0, dt109_14_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
115	t109_14_1, dt109_14_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
116	t109_14_2, dt109_14_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
117	t109_14_3, dt109_14_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
118	t109_14_4, dt109_14_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
119	t109_14_5, dt109_14_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
120	t109_14_6, dt109_14_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
121	t109_14_7, dt109_14_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
122	t109_15_0, dt109_15_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
123	t109_15_1, dt109_15_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
124	t109_15_2, dt109_15_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
125	t109_15_3, dt109_15_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	985
126	t109_15_4, dt109_15_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
127	t109_15_5, dt109_15_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
128	t109_15_6, dt109_15_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
129	t109_15_7, dt109_15_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
130	t109_16_0, dt109_16_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
131	t109_16_1, dt109_16_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
132	t109_16_2, dt109_16_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
133	t109_16_3, dt109_16_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
134	t109_16_4, dt109_16_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
135	t109_16_5, dt109_16_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
136	t109_16_6, dt109_16_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
137	t109_16_7, dt109_16_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
138	t109_17_0, dt109_17_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
139	t109_17_1, dt109_17_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
140	t109_17_2, dt109_17_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
141	t109_17_3, dt109_17_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
142	t109_17_4, dt109_17_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
143	t109_17_5, dt109_17_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
144	t109_17_6, dt109_17_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
145	t109_17_7, dt109_17_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
146	t109_18_0, dt109_18_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
147	t109_18_1, dt109_18_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
148	t109_18_2, dt109_18_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
149	t109_18_3, dt109_18_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
150	t109_18_4, dt109_18_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
151	t109_18_5, dt109_18_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
152	t109_18_6, dt109_18_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
153	t109_18_7, dt109_18_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
154	t109_19_0, dt109_19_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
155	t109_19_1, dt109_19_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
156	t109_19_2, dt109_19_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
157	t109_19_3, dt109_19_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
158	t109_19_4, dt109_19_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
159	t109_19_5, dt109_19_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
160	t109_19_6, dt109_19_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
161	t109_19_7, dt109_19_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
162	t109_20_0, dt109_20_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
163	t109_20_1, dt109_20_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
164	t109_20_2, dt109_20_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
165	t109_20_3, dt109_20_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
166	t109_20_4, dt109_20_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
167	t109_20_5, dt109_20_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
168	t109_20_6, dt109_20_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
169	t109_20_7, dt109_20_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
170	t109_21_0, dt109_21_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
171	t109_21_1, dt109_21_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
172	t109_21_2, dt109_21_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
173	t109_21_3, dt109_21_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
174	t109_21_4, dt109_21_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
175	t109_21_5, dt109_21_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
176	t109_21_6, dt109_21_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
177	t109_21_7, dt109_21_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
178	t109_22_0, dt109_22_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
179	t109_22_1, dt109_22_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
180	t109_22_2, dt109_22_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
181	t109_22_3, dt109_22_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
182	t109_23_0, dt109_23_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
183	t109_23_1, dt109_23_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
184	t109_23_2, dt109_23_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
185	t109_23_3, dt109_23_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
186	t109_24_0, dt109_24_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
187	t109_24_1, dt109_24_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
188	t109_24_2, dt109_24_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
189	t109_24_3, dt109_24_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
190	t109_25_0, dt109_25_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
191	t109_25_1, dt109_25_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
192	t109_25_2, dt109_25_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
193	t109_25_3, dt109_25_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
194	t109_26_0, dt109_26_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
195	t109_26_1, dt109_26_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
196	t109_26_2, dt109_26_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
197	t109_26_3, dt109_26_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
198	t109_27_0, dt109_27_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
199	t109_27_1, dt109_27_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
200	t109_27_2, dt109_27_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
201	t109_27_3, dt109_27_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987

Key to the table

Only one line is displayed for both a plane and its dual, an asterisk (*) in the first column indicating that the plane is self-dual. Each line includes the following information and isomorphism invariants for each plane.

Plane provides a pzip file containing the projective plane. I assume you have installed pzip under linux, which compresses each plane to about 6 KB. Right-click to save as plane.pz, then type the command punzip plane.pz to recover plane as a text file. This text file has 2451 rows, each row specifying a line of the plane as a subset of the points 0,1,2,...,2450. For non-self-dual planes, a second file is also given, containing the dual of the first.
|Autgp| The order of the full collineation group of the projective plane. This table entry is linked to a gzip file providing generators of the automorphism group. Right-click to save as plane.gz, then type the command gunzip plane.gz to recover plane as a text file. This text file lists generators of the full collineation group as permutations of the integers 0,1,2,...,4901 where 0,1,2,...,2450 are labels for the points and 2451,...,4901 are labels for the lines. Generators for the automorphism group of the dual plane are not provided since these are trivially obtained from the generators given for the original plane.
Point Orbits The lengths of the full automorphism group on the points. (These are the lengths of the line orbits for the dual plane.)
Line Orbits The lengths of the full automorphism group on the lines. (These are the lengths of the point orbits for the dual plane.)
7-rank The rank of the (0,1)-incidence matrix of the projective plane, over a field of characteristic 7.

/ revised February, 2011