Projective Planes of Order 49 Related to t104

I am currently compiling a list of known projective planes of order 49. As part of this enumeration, here are listed the plane t104 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 t104

Entry	Plane	\|Autgp\|	Point Orbits	Line Orbits	7-rank
1	Translation Plane t104, dual dt104	57624	1²,2¹⁰,4⁷,2401	1,49²,98¹⁰,196⁷	941
2	t104_0_0, dt104_0_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
3	t104_0_1, dt104_0_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
4	t104_0_2, dt104_0_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
5	t104_0_3, dt104_0_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
6	t104_0_4, dt104_0_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
7	t104_0_5, dt104_0_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
8	t104_0_6, dt104_0_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
9	t104_0_7, dt104_0_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
10	t104_1_0, dt104_1_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
11	t104_1_1, dt104_1_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
12	t104_1_2, dt104_1_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
13	t104_1_3, dt104_1_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
14	t104_1_4, dt104_1_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
15	t104_1_5, dt104_1_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
16	t104_1_6, dt104_1_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
17	t104_1_7, dt104_1_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
18	t104_2_0, dt104_2_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
19	t104_2_1, dt104_2_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
20	t104_2_2, dt104_2_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
21	t104_2_3, dt104_2_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
22	t104_2_4, dt104_2_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
23	t104_2_5, dt104_2_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
24	t104_2_6, dt104_2_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
25	t104_2_7, dt104_2_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
26	t104_3_0, dt104_3_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
27	t104_3_1, dt104_3_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
28	t104_3_2, dt104_3_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
29	t104_3_3, dt104_3_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
30	t104_3_4, dt104_3_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
31	t104_3_5, dt104_3_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
32	t104_3_6, dt104_3_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
33	t104_3_7, dt104_3_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
34	t104_4_0, dt104_4_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
35	t104_4_1, dt104_4_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
36	t104_4_2, dt104_4_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
37	t104_4_3, dt104_4_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
38	t104_4_4, dt104_4_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
39	t104_4_5, dt104_4_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
40	t104_4_6, dt104_4_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
41	t104_4_7, dt104_4_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
42	t104_5_0, dt104_5_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
43	t104_5_1, dt104_5_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
44	t104_5_2, dt104_5_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	985
45	t104_5_3, dt104_5_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
46	t104_5_4, dt104_5_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
47	t104_5_5, dt104_5_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
48	t104_5_6, dt104_5_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
49	t104_5_7, dt104_5_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
50	t104_6_0, dt104_6_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
51	t104_6_1, dt104_6_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
52	t104_6_2, dt104_6_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
53	t104_6_3, dt104_6_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
54	t104_6_4, dt104_6_4	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
55	t104_6_5, dt104_6_5	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
56	t104_6_6, dt104_6_6	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
57	t104_6_7, dt104_6_7	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
58	t104_7_0, dt104_7_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
59	t104_7_1, dt104_7_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
60	t104_7_2, dt104_7_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	985
61	t104_7_3, dt104_7_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
62	t104_8_0, dt104_8_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
63	t104_8_1, dt104_8_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
64	t104_8_2, dt104_8_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
65	t104_8_3, dt104_8_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
66	t104_9_0, dt104_9_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
67	t104_9_1, dt104_9_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
68	t104_9_2, dt104_9_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
69	t104_9_3, dt104_9_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
70	t104_10_0, dt104_10_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
71	t104_10_1, dt104_10_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
72	t104_10_2, dt104_10_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
73	t104_10_3, dt104_10_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
74	t104_11_0, dt104_11_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
75	t104_11_1, dt104_11_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
76	t104_11_2, dt104_11_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
77	t104_11_3, dt104_11_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
78	t104_12_0, dt104_12_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
79	t104_12_1, dt104_12_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
80	t104_12_2, dt104_12_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
81	t104_12_3, dt104_12_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
82	t104_13_0, dt104_13_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
83	t104_13_1, dt104_13_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
84	t104_13_2, dt104_13_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
85	t104_13_3, dt104_13_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
86	t104_14_0, dt104_14_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
87	t104_14_1, dt104_14_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
88	t104_14_2, dt104_14_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
89	t104_14_3, dt104_14_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
90	t104_15_0, dt104_15_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
91	t104_15_1, dt104_15_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
92	t104_15_2, dt104_15_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
93	t104_15_3, dt104_15_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
94	t104_16_0, dt104_16_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
95	t104_16_1, dt104_16_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
96	t104_16_2, dt104_16_2	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
97	t104_16_3, dt104_16_3	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
98	t104_17_0, dt104_17_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
99	t104_17_1, dt104_17_1	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
100	t104_18_0, dt104_18_0	2058	1,7⁵⁶,2058	1⁸,42,49⁴⁹	987
101	t104_18_1, dt104_18_1	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