Projective Planes of Order 49 Related to t54

I am currently compiling a list of known projective planes of order 49. As part of this enumeration, here are listed the plane t54 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 t54

Entry	Plane	\|Autgp\|	Point Orbits	Line Orbits	7-rank
1	Translation Plane t54, dual dt54	28812	1⁴,2²³,2401	1,49⁴,98²³	941
2	t54_0_0, dt54_0_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
3	t54_0_1, dt54_0_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
4	t54_0_2, dt54_0_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
5	t54_0_3, dt54_0_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
6	t54_0_4, dt54_0_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
7	t54_0_5, dt54_0_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
8	t54_0_6, dt54_0_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
9	t54_0_7, dt54_0_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
10	t54_1_0, dt54_1_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
11	t54_1_1, dt54_1_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
12	t54_1_2, dt54_1_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
13	t54_1_3, dt54_1_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
14	t54_1_4, dt54_1_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
15	t54_1_5, dt54_1_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
16	t54_1_6, dt54_1_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
17	t54_1_7, dt54_1_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
18	t54_2_0, dt54_2_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
19	t54_2_1, dt54_2_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
20	t54_2_2, dt54_2_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
21	t54_2_3, dt54_2_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
22	t54_2_4, dt54_2_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
23	t54_2_5, dt54_2_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
24	t54_2_6, dt54_2_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
25	t54_2_7, dt54_2_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
26	t54_3_0, dt54_3_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
27	t54_3_1, dt54_3_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
28	t54_3_2, dt54_3_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
29	t54_3_3, dt54_3_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
30	t54_3_4, dt54_3_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
31	t54_3_5, dt54_3_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
32	t54_3_6, dt54_3_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
33	t54_3_7, dt54_3_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
34	t54_4_0, dt54_4_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
35	t54_4_1, dt54_4_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
36	t54_4_2, dt54_4_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
37	t54_4_3, dt54_4_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
38	t54_4_4, dt54_4_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
39	t54_4_5, dt54_4_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
40	t54_4_6, dt54_4_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
41	t54_4_7, dt54_4_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
42	t54_5_0, dt54_5_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
43	t54_5_1, dt54_5_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
44	t54_5_2, dt54_5_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
45	t54_5_3, dt54_5_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
46	t54_5_4, dt54_5_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
47	t54_5_5, dt54_5_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
48	t54_5_6, dt54_5_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
49	t54_5_7, dt54_5_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
50	t54_6_0, dt54_6_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
51	t54_6_1, dt54_6_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
52	t54_6_2, dt54_6_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
53	t54_6_3, dt54_6_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
54	t54_6_4, dt54_6_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
55	t54_6_5, dt54_6_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
56	t54_6_6, dt54_6_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
57	t54_6_7, dt54_6_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
58	t54_7_0, dt54_7_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
59	t54_7_1, dt54_7_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
60	t54_7_2, dt54_7_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
61	t54_7_3, dt54_7_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
62	t54_7_4, dt54_7_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
63	t54_7_5, dt54_7_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
64	t54_7_6, dt54_7_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
65	t54_7_7, dt54_7_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
66	t54_8_0, dt54_8_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
67	t54_8_1, dt54_8_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
68	t54_8_2, dt54_8_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
69	t54_8_3, dt54_8_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
70	t54_8_4, dt54_8_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
71	t54_8_5, dt54_8_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
72	t54_8_6, dt54_8_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
73	t54_8_7, dt54_8_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
74	t54_9_0, dt54_9_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
75	t54_9_1, dt54_9_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
76	t54_9_2, dt54_9_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
77	t54_9_3, dt54_9_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
78	t54_9_4, dt54_9_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
79	t54_9_5, dt54_9_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
80	t54_9_6, dt54_9_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
81	t54_9_7, dt54_9_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
82	t54_10_0, dt54_10_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
83	t54_10_1, dt54_10_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
84	t54_10_2, dt54_10_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
85	t54_10_3, dt54_10_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
86	t54_10_4, dt54_10_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
87	t54_10_5, dt54_10_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
88	t54_10_6, dt54_10_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
89	t54_10_7, dt54_10_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
90	t54_11_0, dt54_11_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
91	t54_11_1, dt54_11_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
92	t54_11_2, dt54_11_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
93	t54_11_3, dt54_11_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
94	t54_11_4, dt54_11_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
95	t54_11_5, dt54_11_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
96	t54_11_6, dt54_11_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
97	t54_11_7, dt54_11_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
98	t54_12_0, dt54_12_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
99	t54_12_1, dt54_12_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
100	t54_12_2, dt54_12_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
101	t54_12_3, dt54_12_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
102	t54_12_4, dt54_12_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
103	t54_12_5, dt54_12_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
104	t54_12_6, dt54_12_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
105	t54_12_7, dt54_12_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
106	t54_13_0, dt54_13_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
107	t54_13_1, dt54_13_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
108	t54_13_2, dt54_13_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
109	t54_13_3, dt54_13_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
110	t54_13_4, dt54_13_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
111	t54_13_5, dt54_13_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
112	t54_13_6, dt54_13_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
113	t54_13_7, dt54_13_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
114	t54_14_0, dt54_14_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
115	t54_14_1, dt54_14_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
116	t54_14_2, dt54_14_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
117	t54_14_3, dt54_14_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
118	t54_14_4, dt54_14_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
119	t54_14_5, dt54_14_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
120	t54_14_6, dt54_14_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
121	t54_14_7, dt54_14_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
122	t54_15_0, dt54_15_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
123	t54_15_1, dt54_15_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
124	t54_15_2, dt54_15_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
125	t54_15_3, dt54_15_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
126	t54_15_4, dt54_15_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
127	t54_15_5, dt54_15_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
128	t54_15_6, dt54_15_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
129	t54_15_7, dt54_15_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
130	t54_16_0, dt54_16_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
131	t54_16_1, dt54_16_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
132	t54_16_2, dt54_16_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
133	t54_16_3, dt54_16_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
134	t54_16_4, dt54_16_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
135	t54_16_5, dt54_16_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
136	t54_16_6, dt54_16_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
137	t54_16_7, dt54_16_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
138	t54_17_0, dt54_17_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
139	t54_17_1, dt54_17_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
140	t54_17_2, dt54_17_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
141	t54_17_3, dt54_17_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
142	t54_17_4, dt54_17_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
143	t54_17_5, dt54_17_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
144	t54_17_6, dt54_17_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
145	t54_17_7, dt54_17_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
146	t54_18_0, dt54_18_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
147	t54_18_1, dt54_18_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
148	t54_18_2, dt54_18_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
149	t54_18_3, dt54_18_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
150	t54_18_4, dt54_18_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
151	t54_18_5, dt54_18_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
152	t54_18_6, dt54_18_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
153	t54_18_7, dt54_18_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
154	t54_19_0, dt54_19_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
155	t54_19_1, dt54_19_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
156	t54_19_2, dt54_19_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
157	t54_19_3, dt54_19_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
158	t54_19_4, dt54_19_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
159	t54_19_5, dt54_19_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
160	t54_19_6, dt54_19_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
161	t54_19_7, dt54_19_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
162	t54_20_0, dt54_20_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
163	t54_20_1, dt54_20_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
164	t54_20_2, dt54_20_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
165	t54_20_3, dt54_20_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
166	t54_20_4, dt54_20_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
167	t54_20_5, dt54_20_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
168	t54_20_6, dt54_20_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
169	t54_20_7, dt54_20_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
170	t54_21_0, dt54_21_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
171	t54_21_1, dt54_21_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
172	t54_21_2, dt54_21_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
173	t54_21_3, dt54_21_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
174	t54_21_4, dt54_21_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
175	t54_21_5, dt54_21_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
176	t54_21_6, dt54_21_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
177	t54_21_7, dt54_21_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
178	t54_22_0, dt54_22_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
179	t54_22_1, dt54_22_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
180	t54_22_2, dt54_22_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
181	t54_22_3, dt54_22_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
182	t54_22_4, dt54_22_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
183	t54_22_5, dt54_22_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
184	t54_22_6, dt54_22_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	985
185	t54_22_7, dt54_22_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
186	t54_23_0, dt54_23_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
187	t54_23_1, dt54_23_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
188	t54_23_2, dt54_23_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
189	t54_23_3, dt54_23_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
190	t54_24_0, dt54_24_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
191	t54_24_1, dt54_24_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
192	t54_24_2, dt54_24_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
193	t54_24_3, dt54_24_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
194	t54_25_0, dt54_25_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
195	t54_25_1, dt54_25_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
196	t54_25_2, dt54_25_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
197	t54_25_3, dt54_25_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
198	t54_26_0, dt54_26_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
199	t54_26_1, dt54_26_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
200	t54_26_2, dt54_26_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
201	t54_26_3, dt54_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