Projective Planes of Order 49 Related to t111

I am currently compiling a list of known projective planes of order 49. As part of this enumeration, here are listed the plane t111 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 t111

Entry	Plane	\|Autgp\|	Point Orbits	Line Orbits	7-rank
1	Translation Plane t111, dual dt111	28812	1¹²,2¹⁹,2401	1,49¹²,98¹⁹	941
2	t111_0_0, dt111_0_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
3	t111_0_1, dt111_0_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
4	t111_0_2, dt111_0_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
5	t111_0_3, dt111_0_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
6	t111_0_4, dt111_0_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
7	t111_0_5, dt111_0_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
8	t111_0_6, dt111_0_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
9	t111_0_7, dt111_0_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
10	t111_1_0, dt111_1_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
11	t111_1_1, dt111_1_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
12	t111_1_2, dt111_1_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
13	t111_1_3, dt111_1_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
14	t111_1_4, dt111_1_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
15	t111_1_5, dt111_1_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
16	t111_1_6, dt111_1_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
17	t111_1_7, dt111_1_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
18	t111_2_0, dt111_2_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
19	t111_2_1, dt111_2_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
20	t111_2_2, dt111_2_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
21	t111_2_3, dt111_2_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
22	t111_2_4, dt111_2_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
23	t111_2_5, dt111_2_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
24	t111_2_6, dt111_2_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
25	t111_2_7, dt111_2_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
26	t111_3_0, dt111_3_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
27	t111_3_1, dt111_3_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
28	t111_3_2, dt111_3_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
29	t111_3_3, dt111_3_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
30	t111_3_4, dt111_3_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
31	t111_3_5, dt111_3_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
32	t111_3_6, dt111_3_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
33	t111_3_7, dt111_3_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
34	t111_4_0, dt111_4_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
35	t111_4_1, dt111_4_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
36	t111_4_2, dt111_4_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
37	t111_4_3, dt111_4_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
38	t111_4_4, dt111_4_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
39	t111_4_5, dt111_4_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
40	t111_4_6, dt111_4_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
41	t111_4_7, dt111_4_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
42	t111_5_0, dt111_5_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
43	t111_5_1, dt111_5_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
44	t111_5_2, dt111_5_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
45	t111_5_3, dt111_5_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
46	t111_5_4, dt111_5_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
47	t111_5_5, dt111_5_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
48	t111_5_6, dt111_5_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
49	t111_5_7, dt111_5_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
50	t111_6_0, dt111_6_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
51	t111_6_1, dt111_6_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
52	t111_6_2, dt111_6_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
53	t111_6_3, dt111_6_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
54	t111_6_4, dt111_6_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
55	t111_6_5, dt111_6_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
56	t111_6_6, dt111_6_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
57	t111_6_7, dt111_6_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
58	t111_7_0, dt111_7_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
59	t111_7_1, dt111_7_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
60	t111_7_2, dt111_7_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
61	t111_7_3, dt111_7_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
62	t111_7_4, dt111_7_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
63	t111_7_5, dt111_7_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
64	t111_7_6, dt111_7_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
65	t111_7_7, dt111_7_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
66	t111_8_0, dt111_8_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
67	t111_8_1, dt111_8_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
68	t111_8_2, dt111_8_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
69	t111_8_3, dt111_8_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
70	t111_8_4, dt111_8_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
71	t111_8_5, dt111_8_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
72	t111_8_6, dt111_8_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
73	t111_8_7, dt111_8_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
74	t111_9_0, dt111_9_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
75	t111_9_1, dt111_9_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
76	t111_9_2, dt111_9_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
77	t111_9_3, dt111_9_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
78	t111_9_4, dt111_9_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
79	t111_9_5, dt111_9_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
80	t111_9_6, dt111_9_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
81	t111_9_7, dt111_9_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
82	t111_10_0, dt111_10_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
83	t111_10_1, dt111_10_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
84	t111_10_2, dt111_10_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
85	t111_10_3, dt111_10_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
86	t111_10_4, dt111_10_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
87	t111_10_5, dt111_10_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
88	t111_10_6, dt111_10_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
89	t111_10_7, dt111_10_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
90	t111_11_0, dt111_11_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
91	t111_11_1, dt111_11_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
92	t111_11_2, dt111_11_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
93	t111_11_3, dt111_11_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
94	t111_11_4, dt111_11_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
95	t111_11_5, dt111_11_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
96	t111_11_6, dt111_11_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
97	t111_11_7, dt111_11_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
98	t111_12_0, dt111_12_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
99	t111_12_1, dt111_12_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
100	t111_12_2, dt111_12_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
101	t111_12_3, dt111_12_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
102	t111_12_4, dt111_12_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
103	t111_12_5, dt111_12_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
104	t111_12_6, dt111_12_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
105	t111_12_7, dt111_12_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
106	t111_13_0, dt111_13_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
107	t111_13_1, dt111_13_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
108	t111_13_2, dt111_13_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
109	t111_13_3, dt111_13_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
110	t111_13_4, dt111_13_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
111	t111_13_5, dt111_13_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
112	t111_13_6, dt111_13_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
113	t111_13_7, dt111_13_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
114	t111_14_0, dt111_14_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
115	t111_14_1, dt111_14_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
116	t111_14_2, dt111_14_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
117	t111_14_3, dt111_14_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
118	t111_14_4, dt111_14_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
119	t111_14_5, dt111_14_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
120	t111_14_6, dt111_14_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
121	t111_14_7, dt111_14_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
122	t111_15_0, dt111_15_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
123	t111_15_1, dt111_15_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
124	t111_15_2, dt111_15_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
125	t111_15_3, dt111_15_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
126	t111_15_4, dt111_15_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
127	t111_15_5, dt111_15_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
128	t111_15_6, dt111_15_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
129	t111_15_7, dt111_15_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
130	t111_16_0, dt111_16_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
131	t111_16_1, dt111_16_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
132	t111_16_2, dt111_16_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
133	t111_16_3, dt111_16_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
134	t111_16_4, dt111_16_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
135	t111_16_5, dt111_16_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
136	t111_16_6, dt111_16_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
137	t111_16_7, dt111_16_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
138	t111_17_0, dt111_17_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
139	t111_17_1, dt111_17_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
140	t111_17_2, dt111_17_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
141	t111_17_3, dt111_17_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
142	t111_17_4, dt111_17_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
143	t111_17_5, dt111_17_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
144	t111_17_6, dt111_17_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
145	t111_17_7, dt111_17_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
146	t111_18_0, dt111_18_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
147	t111_18_1, dt111_18_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
148	t111_18_2, dt111_18_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
149	t111_18_3, dt111_18_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
150	t111_18_4, dt111_18_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
151	t111_18_5, dt111_18_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
152	t111_18_6, dt111_18_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
153	t111_18_7, dt111_18_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
154	t111_19_0, dt111_19_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
155	t111_19_1, dt111_19_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
156	t111_19_2, dt111_19_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
157	t111_19_3, dt111_19_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
158	t111_20_0, dt111_20_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
159	t111_20_1, dt111_20_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
160	t111_20_2, dt111_20_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
161	t111_20_3, dt111_20_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
162	t111_21_0, dt111_21_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
163	t111_21_1, dt111_21_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
164	t111_21_2, dt111_21_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
165	t111_21_3, dt111_21_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
166	t111_22_0, dt111_22_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
167	t111_22_1, dt111_22_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
168	t111_22_2, dt111_22_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
169	t111_22_3, dt111_22_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
170	t111_23_0, dt111_23_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
171	t111_23_1, dt111_23_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
172	t111_23_2, dt111_23_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
173	t111_23_3, dt111_23_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
174	t111_24_0, dt111_24_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
175	t111_24_1, dt111_24_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
176	t111_24_2, dt111_24_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
177	t111_24_3, dt111_24_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
178	t111_25_0, dt111_25_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
179	t111_25_1, dt111_25_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
180	t111_25_2, dt111_25_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
181	t111_25_3, dt111_25_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
182	t111_26_0, dt111_26_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
183	t111_26_1, dt111_26_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
184	t111_26_2, dt111_26_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
185	t111_26_3, dt111_26_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
186	t111_27_0, dt111_27_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
187	t111_27_1, dt111_27_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
188	t111_27_2, dt111_27_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
189	t111_27_3, dt111_27_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
190	t111_28_0, dt111_28_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
191	t111_28_1, dt111_28_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
192	t111_28_2, dt111_28_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
193	t111_28_3, dt111_28_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
194	t111_29_0, dt111_29_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
195	t111_29_1, dt111_29_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
196	t111_29_2, dt111_29_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
197	t111_29_3, dt111_29_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
198	t111_30_0, dt111_30_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
199	t111_30_1, dt111_30_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
200	t111_30_2, dt111_30_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
201	t111_30_3, dt111_30_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