Projective Planes of Order 49 Related to t114


I am currently compiling a list of known projective planes of order 49. As part of this enumeration, here are listed the plane t114 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 t114

Entry Plane |Autgp| Point Orbits Line Orbits 7-rank
1 Translation Plane t114, dual dt114 230496 2,42,83,16,2401 1,98,1962,3923,784 941
2 t114_0_0, dt114_0_0 2058 1,756,2058 18,42,4949 987
3 t114_0_1, dt114_0_1 2058 1,756,2058 18,42,4949 987
4 t114_0_2, dt114_0_2 2058 1,756,2058 18,42,4949 987
5 t114_0_3, dt114_0_3 2058 1,756,2058 18,42,4949 987
6 t114_0_4, dt114_0_4 2058 1,756,2058 18,42,4949 987
7 t114_0_5, dt114_0_5 2058 1,756,2058 18,42,4949 987
8 t114_0_6, dt114_0_6 2058 1,756,2058 18,42,4949 987
9 t114_0_7, dt114_0_7 2058 1,756,2058 18,42,4949 987
10 t114_1_0, dt114_1_0 2058 1,756,2058 18,42,4949 987
11 t114_1_1, dt114_1_1 2058 1,756,2058 18,42,4949 987
12 t114_1_2, dt114_1_2 2058 1,756,2058 18,42,4949 987
13 t114_1_3, dt114_1_3 2058 1,756,2058 18,42,4949 987
14 t114_2_0, dt114_2_0 2058 1,756,2058 18,42,4949 987
15 t114_2_1, dt114_2_1 2058 1,756,2058 18,42,4949 987
16 t114_2_2, dt114_2_2 2058 1,756,2058 18,42,4949 987
17 t114_2_3, dt114_2_3 2058 1,756,2058 18,42,4949 987
18 t114_3_0, dt114_3_0 2058 1,756,2058 18,42,4949 987
19 t114_3_1, dt114_3_1 2058 1,756,2058 18,42,4949 987
20 t114_3_2, dt114_3_2 2058 1,756,2058 18,42,4949 987
21 t114_3_3, dt114_3_3 2058 1,756,2058 18,42,4949 987
22 t114_4_0, dt114_4_0 2058 1,756,2058 18,42,4949 987
23 t114_4_1, dt114_4_1 2058 1,756,2058 18,42,4949 987
24 t114_5_0, dt114_5_0 2058 1,756,2058 18,42,4949 987
25 t114_5_1, dt114_5_1 2058 1,756,2058 18,42,4949 987
26 t114_6_0, dt114_6_0 4116 1,78,1424,2058 18,42,49,9824 985
27 t114_6_1, dt114_6_1 4116 1,78,1424,2058 18,42,49,9824 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