Centralizers of semisimple elements in G2(q)
--------------------------------------------

|G(q)| = q^6 phi1^2 phi2^2 phi3 phi6

Semisimple class types:
i = 1: Pi = [ 1, 2 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [1,1,1]
      Dynkin type is G_2(q)
      Order of center |Z^F|: 1
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1
        q congruent 2 modulo 6:   1
        q congruent 3 modulo 6:   1
        q congruent 4 modulo 6:   1
        q congruent 5 modulo 6:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 1 .. 6 ]
      elements of other class types in center:
[  ]

i = 2: Pi = [ 1, 12 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [2,1,1]
      Dynkin type is A_2(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 3
        3, q congruent 1 modulo 3
        1, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1
        q congruent 2 modulo 6:   0
        q congruent 3 modulo 6:   0
        q congruent 4 modulo 6:   1
        q congruent 5 modulo 6:   0
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 2, 5 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

    k = 2: F-action on Pi is ( 1,12)      [2,1,2]
      Dynkin type is ^2A_2(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 3
        1, q congruent 1 modulo 3
        3, q congruent 2 modulo 3
      Numbers of classes in class type:
        q congruent 1 modulo 6:   0
        q congruent 2 modulo 6:   1
        q congruent 3 modulo 6:   0
        q congruent 4 modulo 6:   0
        q congruent 5 modulo 6:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 6, 3, 4 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

i = 3: Pi = [ 2, 12 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [3,1,1]
      Dynkin type is A_1(q) + ~A_1(q)
      Order of center |Z^F|: 1 times
        1, q congruent 0 modulo 2
        2, q congruent 1 modulo 2
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1
        q congruent 2 modulo 6:   0
        q congruent 3 modulo 6:   1
        q congruent 4 modulo 6:   0
        q congruent 5 modulo 6:   1
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 3, 2, 6 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ] ]

i = 4: Pi = [ 1 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [4,1,1]
      Dynkin type is A_1(q) + T(phi1)
      Order of center |Z^F|: phi1
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1/2 ( q-5 )
        q congruent 2 modulo 6:   1/2 ( q-2 )
        q congruent 3 modulo 6:   1/2 ( q-3 )
        q congruent 4 modulo 6:   1/2 ( q-4 )
        q congruent 5 modulo 6:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 2 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 1 ] ]

    k = 2: F-action on Pi is ()      [4,1,2]
      Dynkin type is A_1(q) + T(phi2)
      Order of center |Z^F|: phi2
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1/2 phi1
        q congruent 2 modulo 6:   1/2 ( q-2 )
        q congruent 3 modulo 6:   1/2 phi1
        q congruent 4 modulo 6:   1/2 q
        q congruent 5 modulo 6:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 3, 6 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 3, 1, 1, 1 ] ]

i = 5: Pi = [ 2 ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [5,1,1]
      Dynkin type is ~A_1(q) + T(phi1)
      Order of center |Z^F|: phi1
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1/2 ( q-3 )
        q congruent 2 modulo 6:   1/2 ( q-2 )
        q congruent 3 modulo 6:   1/2 ( q-3 )
        q congruent 4 modulo 6:   1/2 ( q-2 )
        q congruent 5 modulo 6:   1/2 ( q-3 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1, 3 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 1 ] ]

    k = 2: F-action on Pi is ()      [5,1,2]
      Dynkin type is ~A_1(q) + T(phi2)
      Order of center |Z^F|: phi2
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1/2 phi1
        q congruent 2 modulo 6:   1/2 q
        q congruent 3 modulo 6:   1/2 phi1
        q congruent 4 modulo 6:   1/2 q
        q congruent 5 modulo 6:   1/2 phi1
      Fusion of maximal tori of C^F in those of G^F:
        [ 2, 6 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 3, 1, 1, 1 ] ]

i = 6: Pi = [  ]
  j = 1: Omega trivial
    k = 1: F-action on Pi is ()      [6,1,1]
      Dynkin type is A_0(q) + T(phi1^2)
      Order of center |Z^F|: phi1^2
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1/12 ( q^2-8*q+19 )
        q congruent 2 modulo 6:   1/12 ( q^2-8*q+12 )
        q congruent 3 modulo 6:   1/12 ( q^2-8*q+15 )
        q congruent 4 modulo 6:   1/12 ( q^2-8*q+16 )
        q congruent 5 modulo 6:   1/12 ( q^2-8*q+15 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 1 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 3 ], [ 4, 1, 1, 6 ], 
  [ 5, 1, 1, 6 ] ]

    k = 2: F-action on Pi is ()      [6,1,2]
      Dynkin type is A_0(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1/4 phi1^2
        q congruent 2 modulo 6:   1/4 q ( q-2 )
        q congruent 3 modulo 6:   1/4 phi1^2
        q congruent 4 modulo 6:   1/4 q ( q-2 )
        q congruent 5 modulo 6:   1/4 phi1^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 2 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ], [ 3, 1, 1, 1 ], [ 4, 1, 1, 2 ], 
  [ 5, 1, 2, 2 ] ]

    k = 3: F-action on Pi is ()      [6,1,3]
      Dynkin type is A_0(q) + T(phi1 phi2)
      Order of center |Z^F|: phi1 phi2
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1/4 phi1^2
        q congruent 2 modulo 6:   1/4 q ( q-2 )
        q congruent 3 modulo 6:   1/4 phi1^2
        q congruent 4 modulo 6:   1/4 q ( q-2 )
        q congruent 5 modulo 6:   1/4 phi1^2
      Fusion of maximal tori of C^F in those of G^F:
        [ 3 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 3, 1, 1, 1 ], [ 4, 1, 2, 2 ], 
  [ 5, 1, 1, 2 ] ]

    k = 4: F-action on Pi is ()      [6,1,4]
      Dynkin type is A_0(q) + T(phi6)
      Order of center |Z^F|: phi6
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1/6 q phi1
        q congruent 2 modulo 6:   1/6 phi2 ( q-2 )
        q congruent 3 modulo 6:   1/6 q phi1
        q congruent 4 modulo 6:   1/6 q phi1
        q congruent 5 modulo 6:   1/6 phi2 ( q-2 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 4 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ] ]

    k = 5: F-action on Pi is ()      [6,1,5]
      Dynkin type is A_0(q) + T(phi3)
      Order of center |Z^F|: phi3
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1/6 phi1 ( q+2 )
        q congruent 2 modulo 6:   1/6 q phi2
        q congruent 3 modulo 6:   1/6 q phi2
        q congruent 4 modulo 6:   1/6 phi1 ( q+2 )
        q congruent 5 modulo 6:   1/6 q phi2
      Fusion of maximal tori of C^F in those of G^F:
        [ 5 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 1, 2 ] ]

    k = 6: F-action on Pi is ()      [6,1,6]
      Dynkin type is A_0(q) + T(phi2^2)
      Order of center |Z^F|: phi2^2
      Numbers of classes in class type:
        q congruent 1 modulo 6:   1/12 phi1 ( q-3 )
        q congruent 2 modulo 6:   1/12 ( q^2-4*q+4 )
        q congruent 3 modulo 6:   1/12 phi1 ( q-3 )
        q congruent 4 modulo 6:   1/12 q ( q-4 )
        q congruent 5 modulo 6:   1/12 ( q^2-4*q+7 )
      Fusion of maximal tori of C^F in those of G^F:
        [ 6 ]
      elements of other class types in center:
[ [ 1, 1, 1, 1 ], [ 2, 1, 2, 2 ], [ 3, 1, 1, 3 ], [ 4, 1, 2, 6 ], 
  [ 5, 1, 2, 6 ] ]