Projective Planes of Order 49 Related to t107

I am currently compiling a list of known projective planes of order 49. As part of this enumeration, here are listed the plane t107 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 t107

Entry	Plane	\|Autgp\|	Point Orbits	Line Orbits	7-rank
1	Translation Plane t107, dual dt107	28812	1⁴,2²³,2401	1,49⁴,98²³	941
2	t107_0_0, dt107_0_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
3	t107_0_1, dt107_0_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
4	t107_0_2, dt107_0_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
5	t107_0_3, dt107_0_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
6	t107_0_4, dt107_0_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
7	t107_0_5, dt107_0_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
8	t107_0_6, dt107_0_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
9	t107_0_7, dt107_0_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
10	t107_1_0, dt107_1_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
11	t107_1_1, dt107_1_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
12	t107_1_2, dt107_1_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
13	t107_1_3, dt107_1_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
14	t107_1_4, dt107_1_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
15	t107_1_5, dt107_1_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
16	t107_1_6, dt107_1_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
17	t107_1_7, dt107_1_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
18	t107_2_0, dt107_2_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
19	t107_2_1, dt107_2_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
20	t107_2_2, dt107_2_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
21	t107_2_3, dt107_2_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
22	t107_2_4, dt107_2_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
23	t107_2_5, dt107_2_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
24	t107_2_6, dt107_2_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
25	t107_2_7, dt107_2_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
26	t107_3_0, dt107_3_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
27	t107_3_1, dt107_3_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
28	t107_3_2, dt107_3_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
29	t107_3_3, dt107_3_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
30	t107_3_4, dt107_3_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
31	t107_3_5, dt107_3_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
32	t107_3_6, dt107_3_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
33	t107_3_7, dt107_3_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
34	t107_4_0, dt107_4_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
35	t107_4_1, dt107_4_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
36	t107_4_2, dt107_4_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
37	t107_4_3, dt107_4_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
38	t107_4_4, dt107_4_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
39	t107_4_5, dt107_4_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
40	t107_4_6, dt107_4_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
41	t107_4_7, dt107_4_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
42	t107_5_0, dt107_5_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
43	t107_5_1, dt107_5_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
44	t107_5_2, dt107_5_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
45	t107_5_3, dt107_5_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
46	t107_5_4, dt107_5_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
47	t107_5_5, dt107_5_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
48	t107_5_6, dt107_5_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
49	t107_5_7, dt107_5_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
50	t107_6_0, dt107_6_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
51	t107_6_1, dt107_6_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
52	t107_6_2, dt107_6_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
53	t107_6_3, dt107_6_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
54	t107_6_4, dt107_6_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
55	t107_6_5, dt107_6_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
56	t107_6_6, dt107_6_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
57	t107_6_7, dt107_6_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
58	t107_7_0, dt107_7_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
59	t107_7_1, dt107_7_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
60	t107_7_2, dt107_7_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
61	t107_7_3, dt107_7_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
62	t107_7_4, dt107_7_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
63	t107_7_5, dt107_7_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
64	t107_7_6, dt107_7_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
65	t107_7_7, dt107_7_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
66	t107_8_0, dt107_8_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
67	t107_8_1, dt107_8_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
68	t107_8_2, dt107_8_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
69	t107_8_3, dt107_8_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
70	t107_8_4, dt107_8_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
71	t107_8_5, dt107_8_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
72	t107_8_6, dt107_8_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
73	t107_8_7, dt107_8_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
74	t107_9_0, dt107_9_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
75	t107_9_1, dt107_9_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
76	t107_9_2, dt107_9_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
77	t107_9_3, dt107_9_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
78	t107_9_4, dt107_9_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
79	t107_9_5, dt107_9_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
80	t107_9_6, dt107_9_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
81	t107_9_7, dt107_9_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
82	t107_10_0, dt107_10_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
83	t107_10_1, dt107_10_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
84	t107_10_2, dt107_10_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
85	t107_10_3, dt107_10_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
86	t107_10_4, dt107_10_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
87	t107_10_5, dt107_10_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
88	t107_10_6, dt107_10_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
89	t107_10_7, dt107_10_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
90	t107_11_0, dt107_11_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
91	t107_11_1, dt107_11_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
92	t107_11_2, dt107_11_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
93	t107_11_3, dt107_11_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
94	t107_11_4, dt107_11_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
95	t107_11_5, dt107_11_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
96	t107_11_6, dt107_11_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
97	t107_11_7, dt107_11_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
98	t107_12_0, dt107_12_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
99	t107_12_1, dt107_12_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
100	t107_12_2, dt107_12_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
101	t107_12_3, dt107_12_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
102	t107_12_4, dt107_12_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
103	t107_12_5, dt107_12_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
104	t107_12_6, dt107_12_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
105	t107_12_7, dt107_12_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
106	t107_13_0, dt107_13_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
107	t107_13_1, dt107_13_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
108	t107_13_2, dt107_13_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
109	t107_13_3, dt107_13_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
110	t107_13_4, dt107_13_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
111	t107_13_5, dt107_13_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
112	t107_13_6, dt107_13_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
113	t107_13_7, dt107_13_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
114	t107_14_0, dt107_14_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
115	t107_14_1, dt107_14_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
116	t107_14_2, dt107_14_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
117	t107_14_3, dt107_14_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
118	t107_14_4, dt107_14_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
119	t107_14_5, dt107_14_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
120	t107_14_6, dt107_14_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
121	t107_14_7, dt107_14_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
122	t107_15_0, dt107_15_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
123	t107_15_1, dt107_15_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
124	t107_15_2, dt107_15_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
125	t107_15_3, dt107_15_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
126	t107_15_4, dt107_15_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
127	t107_15_5, dt107_15_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
128	t107_15_6, dt107_15_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
129	t107_15_7, dt107_15_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
130	t107_16_0, dt107_16_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
131	t107_16_1, dt107_16_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
132	t107_16_2, dt107_16_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
133	t107_16_3, dt107_16_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
134	t107_16_4, dt107_16_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
135	t107_16_5, dt107_16_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
136	t107_16_6, dt107_16_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
137	t107_16_7, dt107_16_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
138	t107_17_0, dt107_17_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
139	t107_17_1, dt107_17_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
140	t107_17_2, dt107_17_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
141	t107_17_3, dt107_17_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
142	t107_17_4, dt107_17_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
143	t107_17_5, dt107_17_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
144	t107_17_6, dt107_17_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
145	t107_17_7, dt107_17_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
146	t107_18_0, dt107_18_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
147	t107_18_1, dt107_18_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
148	t107_18_2, dt107_18_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
149	t107_18_3, dt107_18_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
150	t107_18_4, dt107_18_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
151	t107_18_5, dt107_18_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
152	t107_18_6, dt107_18_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
153	t107_18_7, dt107_18_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
154	t107_19_0, dt107_19_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
155	t107_19_1, dt107_19_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
156	t107_19_2, dt107_19_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
157	t107_19_3, dt107_19_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
158	t107_19_4, dt107_19_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
159	t107_19_5, dt107_19_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
160	t107_19_6, dt107_19_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
161	t107_19_7, dt107_19_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
162	t107_20_0, dt107_20_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
163	t107_20_1, dt107_20_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
164	t107_20_2, dt107_20_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
165	t107_20_3, dt107_20_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
166	t107_20_4, dt107_20_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
167	t107_20_5, dt107_20_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
168	t107_20_6, dt107_20_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
169	t107_20_7, dt107_20_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
170	t107_21_0, dt107_21_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
171	t107_21_1, dt107_21_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
172	t107_21_2, dt107_21_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
173	t107_21_3, dt107_21_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
174	t107_21_4, dt107_21_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
175	t107_21_5, dt107_21_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
176	t107_21_6, dt107_21_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
177	t107_21_7, dt107_21_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
178	t107_22_0, dt107_22_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
179	t107_22_1, dt107_22_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
180	t107_22_2, dt107_22_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
181	t107_22_3, dt107_22_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
182	t107_22_4, dt107_22_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
183	t107_22_5, dt107_22_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
184	t107_22_6, dt107_22_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
185	t107_22_7, dt107_22_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
186	t107_23_0, dt107_23_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
187	t107_23_1, dt107_23_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
188	t107_23_2, dt107_23_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
189	t107_23_3, dt107_23_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
190	t107_24_0, dt107_24_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
191	t107_24_1, dt107_24_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
192	t107_24_2, dt107_24_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
193	t107_24_3, dt107_24_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
194	t107_25_0, dt107_25_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
195	t107_25_1, dt107_25_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
196	t107_25_2, dt107_25_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
197	t107_25_3, dt107_25_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
198	t107_26_0, dt107_26_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
199	t107_26_1, dt107_26_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
200	t107_26_2, dt107_26_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
201	t107_26_3, dt107_26_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