mu = 3
  long: c = (1 2 3) on (1 2 ... L), L >= 3: x c = (1 3 2 4 5 6) ... (L = 6 shown)
  long: c = (1 3 5) on (1 2 ... L), L >= 5: x c = (1 4 5 2 3 6 7 8) ... (L = 8 shown); even conjugator
  tau = 2.1        x = (1 2)                  c = (1 2 3)            x c = (2 3)
  partner of 2^(n/2): local x = (1 2)(3 4) (on 4 points), c = (1 2 3), x c = (2 4 3) (type 3.1)
mu = 2.2
  long: c = (1 3)(2 4) on (1 2 ... L), L >= 4: x c = (1 4 3 2 5 6 7) ... (L = 7 shown)
  long: c = (1 4)(2 6) on (1 2 ... L), L >= 6: x c = (1 5 6 3 4 2 7 8 9) ... (L = 9 shown); even conjugator
  tau = 3.1        x = (1 2 3)                c = (1 2)(3 4)         x c = (1 3 4)
  tau = 3.2        x = (1 2 3)(4 5)           c = (1 4)(2 5)         x c = (1 5 3)(2 4)
  tau = 3.3        x = (1 2 3)(4 5 6)         c = (1 4)(2 5)         x c = (1 5 3)(2 6 4)
  tau = 2.2        x = (1 2)(3 4)             c = (1 3)(2 4)         x c = (1 4)(2 3)
mu = 5
  long: c = (1 2 3 4 5) on (1 2 ... L), L >= 5: x c = (1 3 5 2 4 6 7 8) ... (L = 8 shown)
  long: c = (1 2 3 5 6) on (1 2 ... L), L >= 6: x c = (1 3 6 2 4 5 7 8 9) ... (L = 9 shown); even conjugator
  tau = 4.1        x = (1 2 3 4)              c = (1 2 4 3 5)        x c = (1 3 5 2)
  tau = 4.2        x = (1 2 3 4)(5 6)         c = (1 2 3 4 5)        x c = (1 3)(2 4 6 5)
  tau = 4.3        x = (1 2 3 4)(5 6 7)       c = (1 2 4 5 3)        x c = (1 3 2)(4 6 7 5)
  tau = 4.4        x = (1 2 3 4)(5 6 7 8)     c = (1 2 5 3 8)        x c = (1 3 5 4)(2 6 7 8)
  tau = 3.3        x = (1 2 3)(4 5 6)         c = (1 2 4 3 6)        x c = (1 3 4)(2 5 6)
  tau = 3.2        x = (1 2 3)(4 5)           c = (1 2 4 3 5)        x c = (1 3 4)(2 5)
  tau = 3.1.1      x = (1 2 3)                c = (1 3 2 4 5)        x c = (2 4 5)
  tau = 2.2.1      x = (1 2)(3 4)             c = (1 2 3 5 4)        x c = (2 4)(3 5)
  partner of 2^(n/2): local x = (1 2)(3 4)(5 6) (on 6 points), c = (1 2 3 5 4), x c = (2 4)(3 6 5) (type 3.2.1)
mu = 3.3
  long: c = (1 2 3)(4 5 6) on (1 2 ... L), L >= 6: x c = (1 3 2 4 6 5 7 8 9) ... (L = 9 shown); even conjugator
  tau = 5.1        x = (1 2 3 4 5)            c = (1 2 3)(4 6 5)     x c = (1 3 2 4 6)
  tau = 5.2        x = (1 2 3 4 5)(6 7)       c = (1 2 4)(3 5 6)     x c = (1 3)(2 5 7 6 4)
  tau = 5.3        x = (1 2 3 4 5)(6 7 8)     c = (1 2 3)(6 7 8)     x c = (1 3 2 4 5)(6 8 7)
  tau = 5.4        x = (1 2 3 4 5)(6 7 8 9)   c = (1 2 3)(4 5 6)     x c = (1 3 2 4)(5 7 8 9 6)
  tau = 5.5        x = (1 2 3 4 5)(6 7 8 9 10) c = (1 2 3)(6 7 8)     x c = (1 3 2 4 5)(6 8 7 9 10)
  tau = 4.1.1      x = (1 2 3 4)              c = (1 3 2)(4 5 6)     x c = (1 4 5 6)
  tau = 4.2        x = (1 2 3 4)(5 6)         c = (1 2 5)(3 4 6)     x c = (1 3)(2 6 4 5)
  tau = 4.3        x = (1 2 3 4)(5 6 7)       c = (1 2 3)(5 6 7)     x c = (1 3 2 4)(5 7 6)
  tau = 4.4        x = (1 2 3 4)(5 6 7 8)     c = (1 2 3)(5 6 7)     x c = (1 3 2 4)(5 7 6 8)
  tau = 3.3        x = (1 2 3)(4 5 6)         c = (1 2 3)(4 5 6)     x c = (1 3 2)(4 6 5)
  tau = 3.2.2      x = (1 2 3)(4 5)(6 7)      c = (1 4 6)(2 7 5)     x c = (1 5 3)(2 6)(4 7)
  tau = 3.2.1      x = (1 2 3)(4 5)           c = (1 2 3)(4 5 6)     x c = (1 3 2)(5 6)
  tau = 3.1.1.1    x = (1 2 3)                c = (1 3 2)(4 5 6)     x c = (4 5 6)
  tau = 2.2.2      x = (1 2)(3 4)(5 6)        c = (1 3 5)(2 6 4)     x c = (1 4)(2 5)(3 6)
  tau = 2.2.1.1    x = (1 2)(3 4)             c = (1 2 5)(3 4 6)     x c = (2 5)(4 6)
mu = 4.2
  long: c = (1 2 3 5)(4 6) on (1 2 ... L), L >= 6: x c = (1 3 6 5 2 4 7 8 9) ... (L = 9 shown); even conjugator
  tau = 5.1        x = (1 2 3 4 5)            c = (1 2 3 6)(4 5)     x c = (1 3 6 2 4)
  tau = 5.2        x = (1 2 3 4 5)(6 7)       c = (1 2 3 4)(5 6)     x c = (1 3 5 7 6)(2 4)
  tau = 5.3        x = (1 2 3 4 5)(6 7 8)     c = (1 2 3 6)(4 8)     x c = (1 3 7 8 5)(2 4 6)
  tau = 5.4        x = (1 2 3 4 5)(6 7 8 9)   c = (1 2 3 6)(4 7)     x c = (1 3 7 5)(2 4 8 9 6)
  tau = 5.5        x = (1 2 3 4 5)(6 7 8 9 10) c = (1 2 3 6)(4 8)     x c = (1 3 7 8 5)(2 4 9 10 6)
  tau = 4.1.1      x = (1 2 3 4)              c = (1 4 3 5)(2 6)     x c = (2 6 3 5)
  tau = 4.2        x = (1 2 3 4)(5 6)         c = (1 2 4 5)(3 6)     x c = (1 3 5 2)(4 6)
  tau = 4.3        x = (1 2 3 4)(5 6 7)       c = (1 2 3 5)(4 6)     x c = (1 3 6)(2 4 7 5)
  tau = 4.4        x = (1 2 3 4)(5 6 7 8)     c = (1 2 3 5)(4 7)     x c = (1 3 6 7)(2 4 8 5)
  tau = 3.2.1      x = (1 2 3)(4 5)           c = (1 2 4 5)(3 6)     x c = (1 3 6)(2 5)
  tau = 3.2.2      x = (1 2 3)(4 5)(6 7)      c = (1 2 4 6)(5 7)     x c = (1 3)(2 5 6)(4 7)
  tau = 3.3.1      x = (1 2 3)(4 5 6)         c = (1 2 4 6)(3 7)     x c = (1 3 7)(2 5 6)
  tau = 3.3.2      x = (1 2 3)(4 5 6)(7 8)    c = (1 2 4 7)(5 8)     x c = (1 3)(2 5 7)(4 8 6)
  tau = 2.2.1.1    x = (1 2)(3 4)             c = (1 2 3 4)(5 6)     x c = (2 4)(5 6)
  partner of 2^(n/2): local x = (1 2)(3 4)(5 6) (on 6 points), c = (1 2 3 5)(4 6), x c = (2 4 5)(3 6) (type 3.2.1)
  partner of 2^((n-1)/2)1: local x = (1 2)(3 4)(5 6) (on 7 points), c = (1 2 3 4)(5 7), x c = (2 4)(5 7 6) (type 3.2.1.1)
  partner of 3^(n/3): local x = (1 2 3)(4 5 6) (on 6 points), c = (1 2 3 4)(5 6), x c = (1 3 5 4 2) (type 5.1)
