Computing non-isomorphic 2-factorizations of K₁₁ of type F⁵

1. Generation -- we started with 15 non-isomorphic disjoint pairs of  F-type 2-factors and generated all F-type 2-factors disjoint with a given start:
   start 0 -- we generated 168 2-factors
   start 1 -- we generated 189 2-factors
   start 2 -- we generated 203 2-factors
   start 3 -- we generated 202 2-factors
   start 4 -- we generated 207 2-factors
   start 5 -- we generated 210 2-factors
   start 6 -- we generated 206 2-factors
   start 7 -- we generated 191 2-factors
   start 8 -- we generated 189 2-factors
   start 9 -- we generated 190 2-factors
   start 10 -- we generated 178 2-factors
   start 11 -- we generated 1 2-factors
   start 12 -- we generated 210 2-factors
   start 13 -- we generated 214 2-factors
   start 15 -- we generated 220 2-factors
2. For each start we computed all systems of three disjoint F-type 2-factors using the sets generated in the previous step.
   start 0 -- we generated 4 disjoint systems
   start 1 -- we generated 3 disjoint systems
   start 2 -- we generated 2 disjoint systems
   start 3 -- we generated 3 disjoint systems
   start 4 -- we generated 3 disjoint systems
   start 5 -- we generated 16 disjoint systems
   start 6 -- we generated 9 disjoint systems
   start 7 -- we generated 4 disjoint systems
   start 8 -- we generated 6 disjoint systems
   start 9 -- we generated 17 disjoint systems
   start 10 -- we generated no disjoint system
   start 11 -- we generated 17 disjoint systems
   start 12 -- we generated 1 disjoint system
   start 13 -- we generated 9 disjoint systems
   start 14 -- we generated 24 disjoint systems
3. The sets obtained in the previous step were partitioned into classes of isomorphisms, referred to as "buckets".
   start 0 --  we got 1 bucket
   start 1 --  we got 2 buckets
   start 2 --  we got 2 buckets
   start 3 --  we got 2 buckets
   start 4 --  we got 3 buckets
   start 5 --  we got 5 buckets
   start 6 --  we got 4 buckets
   start 7 --  we got 1 bucket
   start 8 --  we got 2 buckets
   start 9 --  we got 3 buckets
   start 11 --  we got 5 buckets
   start 12 --  we got 1 bucket
   start 13 --  we got 3 buckets
   start 14 --  we got 3 buckets
4. From each bucket obtained in the previous step we chose a single representative, i.e. 37 systems
5. The set from the previous step was partitioned into classes of isomorphism (buckets), obtaining 11 buckets.
6. From each bucket we chose a representative, to obtain 11 non-isomorphic systems of type F⁵
7. For each system, using the same program for finding isomorphisms, the group of automorphisms was computed obtaining in the group sizes.