Projective Planes of Order 49 Related to t118


I am currently compiling a list of known projective planes of order 49. As part of this enumeration, here are listed the plane t118 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 t118

Entry Plane |Autgp| Point Orbits Line Orbits 7-rank
1 Translation Plane t118, dual dt118 115248 14,25,43,83,2401 1,494,985,1963,3923 941
2 t118_0_0, dt118_0_0 2058 1,756,2058 18,42,4949 987
3 t118_0_1, dt118_0_1 2058 1,756,2058 18,42,4949 987
4 t118_0_2, dt118_0_2 2058 1,756,2058 18,42,4949 987
5 t118_0_3, dt118_0_3 2058 1,756,2058 18,42,4949 987
6 t118_0_4, dt118_0_4 2058 1,756,2058 18,42,4949 987
7 t118_0_5, dt118_0_5 2058 1,756,2058 18,42,4949 987
8 t118_0_6, dt118_0_6 2058 1,756,2058 18,42,4949 987
9 t118_0_7, dt118_0_7 2058 1,756,2058 18,42,4949 987
10 t118_1_0, dt118_1_0 2058 1,756,2058 18,42,4949 987
11 t118_1_1, dt118_1_1 2058 1,756,2058 18,42,4949 987
12 t118_1_2, dt118_1_2 2058 1,756,2058 18,42,4949 987
13 t118_1_3, dt118_1_3 2058 1,756,2058 18,42,4949 987
14 t118_1_4, dt118_1_4 2058 1,756,2058 18,42,4949 987
15 t118_1_5, dt118_1_5 2058 1,756,2058 18,42,4949 987
16 t118_1_6, dt118_1_6 2058 1,756,2058 18,42,4949 987
17 t118_1_7, dt118_1_7 2058 1,756,2058 18,42,4949 987
18 t118_2_0, dt118_2_0 2058 1,756,2058 18,42,4949 987
19 t118_2_1, dt118_2_1 2058 1,756,2058 18,42,4949 987
20 t118_2_2, dt118_2_2 2058 1,756,2058 18,42,4949 987
21 t118_2_3, dt118_2_3 2058 1,756,2058 18,42,4949 987
22 t118_2_4, dt118_2_4 2058 1,756,2058 18,42,4949 987
23 t118_2_5, dt118_2_5 2058 1,756,2058 18,42,4949 987
24 t118_2_6, dt118_2_6 2058 1,756,2058 18,42,4949 987
25 t118_2_7, dt118_2_7 2058 1,756,2058 18,42,4949 987
26 t118_3_0, dt118_3_0 2058 1,756,2058 18,42,4949 987
27 t118_3_1, dt118_3_1 2058 1,756,2058 18,42,4949 987
28 t118_3_2, dt118_3_2 2058 1,756,2058 18,42,4949 987
29 t118_3_3, dt118_3_3 2058 1,756,2058 18,42,4949 987
30 t118_4_0, dt118_4_0 2058 1,756,2058 18,42,4949 987
31 t118_4_1, dt118_4_1 2058 1,756,2058 18,42,4949 987
32 t118_4_2, dt118_4_2 2058 1,756,2058 18,42,4949 987
33 t118_4_3, dt118_4_3 2058 1,756,2058 18,42,4949 987
34 t118_5_0, dt118_5_0 2058 1,756,2058 18,42,4949 987
35 t118_5_1, dt118_5_1 2058 1,756,2058 18,42,4949 987
36 t118_5_2, dt118_5_2 2058 1,756,2058 18,42,4949 987
37 t118_5_3, dt118_5_3 2058 1,756,2058 18,42,4949 987
38 t118_6_0, dt118_6_0 2058 1,756,2058 18,42,4949 987
39 t118_6_1, dt118_6_1 2058 1,756,2058 18,42,4949 987
40 t118_7_0, dt118_7_0 2058 1,756,2058 18,42,4949 987
41 t118_7_1, dt118_7_1 2058 1,756,2058 18,42,4949 987
42 t118_8_0, dt118_8_0 2058 1,756,2058 18,42,4949 987
43 t118_8_1, dt118_8_1 2058 1,756,2058 18,42,4949 987
44 t118_9_0, dt118_9_0 2058 1,756,2058 18,42,4949 987
45 t118_9_1, dt118_9_1 2058 1,756,2058 18,42,4949 987
46 t118_10_0, dt118_10_0 2058 1,756,2058 18,42,4949 987
47 t118_10_1, dt118_10_1 2058 1,756,2058 18,42,4949 987
48 t118_11_0, dt118_11_0 2058 1,756,2058 18,42,4949 987
49 t118_12_0, dt118_12_0 2058 1,756,2058 18,42,4949 987
50 t118_13_0, dt118_13_0 2058 1,756,2058 18,42,4949 987
51 t118_14_0, dt118_14_0 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.


/ revised February, 2011