Projective Planes of Order 49 Related to t76

I am currently compiling a list of known projective planes of order 49. As part of this enumeration, here are listed the plane t76 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 t76

Entry	Plane	\|Autgp\|	Point Orbits	Line Orbits	7-rank
1	Translation Plane t76, dual dt76	28812	1⁴,2²³,2401	1,49⁴,98²³	941
2	t76_0_0, dt76_0_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
3	t76_0_1, dt76_0_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
4	t76_0_2, dt76_0_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
5	t76_0_3, dt76_0_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
6	t76_0_4, dt76_0_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
7	t76_0_5, dt76_0_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
8	t76_0_6, dt76_0_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
9	t76_0_7, dt76_0_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
10	t76_1_0, dt76_1_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
11	t76_1_1, dt76_1_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
12	t76_1_2, dt76_1_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
13	t76_1_3, dt76_1_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
14	t76_1_4, dt76_1_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
15	t76_1_5, dt76_1_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
16	t76_1_6, dt76_1_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
17	t76_1_7, dt76_1_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
18	t76_2_0, dt76_2_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
19	t76_2_1, dt76_2_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
20	t76_2_2, dt76_2_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
21	t76_2_3, dt76_2_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
22	t76_2_4, dt76_2_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
23	t76_2_5, dt76_2_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
24	t76_2_6, dt76_2_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
25	t76_2_7, dt76_2_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
26	t76_3_0, dt76_3_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
27	t76_3_1, dt76_3_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
28	t76_3_2, dt76_3_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
29	t76_3_3, dt76_3_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
30	t76_3_4, dt76_3_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
31	t76_3_5, dt76_3_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
32	t76_3_6, dt76_3_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
33	t76_3_7, dt76_3_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
34	t76_4_0, dt76_4_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
35	t76_4_1, dt76_4_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
36	t76_4_2, dt76_4_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
37	t76_4_3, dt76_4_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
38	t76_4_4, dt76_4_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
39	t76_4_5, dt76_4_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
40	t76_4_6, dt76_4_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
41	t76_4_7, dt76_4_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
42	t76_5_0, dt76_5_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
43	t76_5_1, dt76_5_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
44	t76_5_2, dt76_5_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
45	t76_5_3, dt76_5_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
46	t76_5_4, dt76_5_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
47	t76_5_5, dt76_5_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
48	t76_5_6, dt76_5_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
49	t76_5_7, dt76_5_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
50	t76_6_0, dt76_6_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
51	t76_6_1, dt76_6_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
52	t76_6_2, dt76_6_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
53	t76_6_3, dt76_6_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
54	t76_6_4, dt76_6_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
55	t76_6_5, dt76_6_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
56	t76_6_6, dt76_6_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
57	t76_6_7, dt76_6_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
58	t76_7_0, dt76_7_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
59	t76_7_1, dt76_7_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
60	t76_7_2, dt76_7_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
61	t76_7_3, dt76_7_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
62	t76_7_4, dt76_7_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
63	t76_7_5, dt76_7_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
64	t76_7_6, dt76_7_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
65	t76_7_7, dt76_7_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
66	t76_8_0, dt76_8_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
67	t76_8_1, dt76_8_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
68	t76_8_2, dt76_8_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
69	t76_8_3, dt76_8_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
70	t76_8_4, dt76_8_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
71	t76_8_5, dt76_8_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
72	t76_8_6, dt76_8_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
73	t76_8_7, dt76_8_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
74	t76_9_0, dt76_9_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
75	t76_9_1, dt76_9_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
76	t76_9_2, dt76_9_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
77	t76_9_3, dt76_9_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
78	t76_9_4, dt76_9_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
79	t76_9_5, dt76_9_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
80	t76_9_6, dt76_9_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
81	t76_9_7, dt76_9_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
82	t76_10_0, dt76_10_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
83	t76_10_1, dt76_10_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
84	t76_10_2, dt76_10_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
85	t76_10_3, dt76_10_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
86	t76_10_4, dt76_10_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
87	t76_10_5, dt76_10_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
88	t76_10_6, dt76_10_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
89	t76_10_7, dt76_10_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
90	t76_11_0, dt76_11_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
91	t76_11_1, dt76_11_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
92	t76_11_2, dt76_11_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
93	t76_11_3, dt76_11_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
94	t76_11_4, dt76_11_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
95	t76_11_5, dt76_11_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
96	t76_11_6, dt76_11_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
97	t76_11_7, dt76_11_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
98	t76_12_0, dt76_12_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
99	t76_12_1, dt76_12_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
100	t76_12_2, dt76_12_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
101	t76_12_3, dt76_12_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
102	t76_12_4, dt76_12_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
103	t76_12_5, dt76_12_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
104	t76_12_6, dt76_12_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
105	t76_12_7, dt76_12_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
106	t76_13_0, dt76_13_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
107	t76_13_1, dt76_13_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
108	t76_13_2, dt76_13_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
109	t76_13_3, dt76_13_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
110	t76_13_4, dt76_13_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
111	t76_13_5, dt76_13_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
112	t76_13_6, dt76_13_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
113	t76_13_7, dt76_13_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
114	t76_14_0, dt76_14_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
115	t76_14_1, dt76_14_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
116	t76_14_2, dt76_14_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
117	t76_14_3, dt76_14_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
118	t76_14_4, dt76_14_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
119	t76_14_5, dt76_14_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
120	t76_14_6, dt76_14_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
121	t76_14_7, dt76_14_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
122	t76_15_0, dt76_15_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
123	t76_15_1, dt76_15_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
124	t76_15_2, dt76_15_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
125	t76_15_3, dt76_15_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
126	t76_15_4, dt76_15_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
127	t76_15_5, dt76_15_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
128	t76_15_6, dt76_15_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
129	t76_15_7, dt76_15_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
130	t76_16_0, dt76_16_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
131	t76_16_1, dt76_16_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
132	t76_16_2, dt76_16_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
133	t76_16_3, dt76_16_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
134	t76_16_4, dt76_16_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
135	t76_16_5, dt76_16_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
136	t76_16_6, dt76_16_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
137	t76_16_7, dt76_16_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
138	t76_17_0, dt76_17_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
139	t76_17_1, dt76_17_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
140	t76_17_2, dt76_17_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
141	t76_17_3, dt76_17_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
142	t76_17_4, dt76_17_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
143	t76_17_5, dt76_17_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
144	t76_17_6, dt76_17_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
145	t76_17_7, dt76_17_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
146	t76_18_0, dt76_18_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
147	t76_18_1, dt76_18_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
148	t76_18_2, dt76_18_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
149	t76_18_3, dt76_18_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
150	t76_18_4, dt76_18_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
151	t76_18_5, dt76_18_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
152	t76_18_6, dt76_18_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
153	t76_18_7, dt76_18_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
154	t76_19_0, dt76_19_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
155	t76_19_1, dt76_19_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
156	t76_19_2, dt76_19_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
157	t76_19_3, dt76_19_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
158	t76_19_4, dt76_19_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
159	t76_19_5, dt76_19_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
160	t76_19_6, dt76_19_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
161	t76_19_7, dt76_19_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
162	t76_20_0, dt76_20_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
163	t76_20_1, dt76_20_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
164	t76_20_2, dt76_20_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
165	t76_20_3, dt76_20_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
166	t76_20_4, dt76_20_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
167	t76_20_5, dt76_20_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
168	t76_20_6, dt76_20_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
169	t76_20_7, dt76_20_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
170	t76_21_0, dt76_21_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
171	t76_21_1, dt76_21_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
172	t76_21_2, dt76_21_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
173	t76_21_3, dt76_21_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
174	t76_21_4, dt76_21_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
175	t76_21_5, dt76_21_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
176	t76_21_6, dt76_21_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
177	t76_21_7, dt76_21_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
178	t76_22_0, dt76_22_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
179	t76_22_1, dt76_22_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
180	t76_22_2, dt76_22_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
181	t76_22_3, dt76_22_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
182	t76_22_4, dt76_22_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
183	t76_22_5, dt76_22_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
184	t76_22_6, dt76_22_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
185	t76_22_7, dt76_22_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
186	t76_23_0, dt76_23_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
187	t76_23_1, dt76_23_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
188	t76_23_2, dt76_23_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
189	t76_23_3, dt76_23_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
190	t76_24_0, dt76_24_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
191	t76_24_1, dt76_24_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
192	t76_24_2, dt76_24_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
193	t76_24_3, dt76_24_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
194	t76_25_0, dt76_25_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
195	t76_25_1, dt76_25_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
196	t76_25_2, dt76_25_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
197	t76_25_3, dt76_25_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
198	t76_26_0, dt76_26_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
199	t76_26_1, dt76_26_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
200	t76_26_2, dt76_26_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
201	t76_26_3, dt76_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