Cohomology of group number 641 of order 128

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128


General information on the group

  • The group has 3 minimal generators and exponent 8.
  • It is non-abelian.
  • It has p-Rank 3.
  • Its center has rank 1.
  • It has 3 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 3.


Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 3 and depth 1.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 1) · (t13  −  2·t12  +  2·t11  −  t10  +  2·t9  +  t8  −  2·t7  +  3·t6  −  3·t5  +  3·t4  −  2·t3  +  2·t2  +  1)

    (t  −  1)3 · (t2  +  1) · (t4  +  1) · (t8  +  1)
  • The a-invariants are -∞,-9,-3,-3. They were obtained using the filter regular HSOP of the Benson test.

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Ring generators

The cohomology ring has 15 minimal generators of maximal degree 16:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_1, a nilpotent element of degree 1
  3. b_1_2, an element of degree 1
  4. a_2_3, a nilpotent element of degree 2
  5. b_2_4, an element of degree 2
  6. b_2_5, an element of degree 2
  7. b_2_6, an element of degree 2
  8. b_5_19, an element of degree 5
  9. b_5_20, an element of degree 5
  10. a_9_29, a nilpotent element of degree 9
  11. b_9_41, an element of degree 9
  12. b_9_44, an element of degree 9
  13. a_10_39, a nilpotent element of degree 10
  14. b_10_53, an element of degree 10
  15. c_16_113, a Duflot regular element of degree 16

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Ring relations

There are 64 minimal relations of maximal degree 20:

  1. a_1_12 + a_1_02
  2. a_1_0·a_1_1 + a_1_02
  3. a_1_0·b_1_2
  4. a_2_3·a_1_1 + a_2_3·a_1_0
  5. b_2_4·a_1_1 + a_2_3·b_1_2 + a_2_3·a_1_1
  6. b_2_4·a_1_0 + a_2_3·a_1_1
  7. b_2_5·b_1_2 + b_2_4·b_1_2 + b_2_6·a_1_1 + b_2_6·a_1_0 + a_1_03
  8. a_2_3·b_1_22 + a_2_3·b_2_4 + a_2_32
  9. b_2_5·a_1_02 + a_2_32 + a_2_3·a_1_02
  10. b_2_4·b_1_22 + b_2_42 + b_2_6·a_1_1·b_1_2 + a_2_3·b_1_22 + a_2_32
  11. b_2_62·a_1_1 + b_2_62·a_1_0 + b_2_5·b_2_6·a_1_1 + b_2_5·b_2_6·a_1_0
       + a_2_3·b_2_6·b_1_2 + a_2_32·a_1_0
  12. b_1_2·b_5_19 + b_2_6·b_1_24 + b_2_62·b_1_22 + b_2_4·b_2_62 + b_2_6·a_1_1·b_1_23
       + a_2_3·b_2_62 + a_2_3·b_2_42 + a_2_33
  13. b_2_4·b_2_52 + b_2_43 + a_1_1·b_5_19 + a_1_0·b_5_19 + b_2_6·a_1_1·b_1_23
       + a_2_3·b_2_52 + a_2_3·b_2_42
  14. a_1_1·b_5_20 + a_2_3·b_2_62 + a_2_3·b_2_5·b_2_6 + a_2_3·b_2_4·b_2_6 + a_2_3·b_2_42
       + a_2_3·b_2_6·a_1_02
  15. a_1_0·b_5_20 + a_2_3·b_2_62 + a_2_3·b_2_5·b_2_6 + a_2_3·b_2_4·b_2_6
       + a_2_3·b_2_6·a_1_02
  16. b_2_4·b_5_19 + b_2_42·b_2_6·b_1_2 + a_2_3·b_5_19 + a_2_3·b_2_4·b_2_6·b_1_2
       + a_2_3·b_2_42·b_1_2 + b_2_62·a_1_03 + a_2_32·b_2_6·a_1_0 + a_2_32·b_2_5·a_1_0
       + a_2_3·b_2_6·a_1_03
  17. b_2_5·b_2_62·a_1_0 + b_2_52·b_2_6·a_1_0 + a_2_3·b_5_20 + a_2_3·b_2_42·b_1_2
       + a_2_3·b_2_62·a_1_0 + b_2_62·a_1_03 + a_2_32·b_2_6·a_1_0
  18. a_2_32·b_2_62·a_1_0 + a_2_32·b_2_5·b_2_6·a_1_0
  19. b_2_4·b_2_5·b_5_20 + b_2_42·b_5_20 + a_2_3·b_2_5·b_5_20 + a_2_3·b_2_42·b_2_6·b_1_2
       + a_2_3·b_2_43·b_1_2 + a_2_32·b_5_20 + a_2_3·a_1_02·b_5_19
  20. b_5_202 + b_2_64·b_1_22 + b_2_5·b_2_64 + b_2_53·b_2_62 + b_2_4·b_2_64
       + b_2_43·b_2_62 + b_2_45 + b_2_5·b_2_6·a_1_1·b_5_19 + b_2_5·b_2_6·a_1_0·b_5_19
       + a_2_3·b_2_52·b_2_62 + a_2_3·b_2_43·b_2_6 + a_2_3·b_2_44 + b_2_64·a_1_02
       + a_2_32·a_1_0·b_5_19 + a_2_33·b_2_5·b_2_6
  21. a_1_1·a_9_29 + b_2_64·a_1_02 + a_2_3·b_2_6·a_1_0·b_5_19 + a_2_32·b_2_63
       + a_2_32·b_2_53 + a_2_33·b_2_52
  22. a_1_0·a_9_29 + b_2_64·a_1_02 + a_2_3·b_2_6·a_1_0·b_5_19 + a_2_32·b_2_63
       + a_2_32·b_2_53 + a_2_33·b_2_62 + a_2_33·b_2_5·b_2_6 + a_2_33·b_2_52
  23. b_5_192 + b_2_6·b_1_23·b_5_20 + b_2_62·b_1_26 + b_2_63·b_1_24
       + b_2_64·b_1_22 + b_2_5·b_2_64 + b_2_54·b_2_6 + b_2_4·b_2_6·b_1_2·b_5_20
       + b_2_42·b_2_63 + b_2_44·b_2_6 + b_1_2·a_9_29 + a_1_1·b_9_41 + b_2_62·a_1_0·b_5_19
       + b_2_5·b_2_6·a_1_1·b_5_19 + b_2_52·a_1_1·b_5_19 + b_2_52·a_1_0·b_5_19
       + b_2_64·a_1_02 + a_2_3·b_2_6·a_1_0·b_5_19 + a_2_3·b_2_5·a_1_0·b_5_19
       + a_2_32·b_2_5·b_2_62 + a_2_32·b_2_53 + a_2_3·b_2_63·a_1_02
       + a_2_32·a_1_0·b_5_19 + a_2_33·b_2_5·b_2_6 + a_2_33·b_2_52
  24. b_5_192 + b_2_62·b_1_26 + b_2_64·b_1_22 + b_2_5·b_2_64 + b_2_54·b_2_6
       + b_2_44·b_2_6 + a_1_0·b_9_41 + b_2_62·a_1_0·b_5_19 + b_2_5·b_2_6·a_1_1·b_5_19
       + b_2_64·a_1_02 + a_2_3·b_2_6·a_1_0·b_5_19 + a_2_3·b_2_5·a_1_0·b_5_19
       + a_2_32·b_2_63 + a_2_32·b_2_5·b_2_62 + a_2_32·b_2_53 + a_2_3·b_2_63·a_1_02
       + a_2_33·b_2_5·b_2_6 + a_2_33·b_2_52
  25. b_1_2·b_9_44 + b_1_2·b_9_41 + b_2_6·b_1_28 + b_2_62·b_1_2·b_5_20 + b_2_64·b_1_22
       + b_2_4·b_2_64 + b_2_42·b_1_2·b_5_20 + b_2_42·b_2_63 + b_2_43·b_2_62 + b_2_45
       + b_1_2·a_9_29 + a_2_3·b_2_64 + a_2_32·b_2_63 + a_2_3·b_2_63·a_1_02
       + a_2_33·b_2_62
  26. b_2_6·b_1_23·b_5_20 + b_2_63·b_1_24 + b_2_4·b_2_6·b_1_2·b_5_20 + b_2_42·b_2_63
       + b_1_2·a_9_29 + a_1_1·b_9_44 + b_2_6·a_1_1·b_1_27 + b_2_62·a_1_0·b_5_19
       + b_2_5·b_2_6·a_1_0·b_5_19 + a_2_3·b_2_64 + a_2_3·b_2_52·b_2_62
       + a_2_3·b_2_43·b_2_6 + a_2_3·b_2_5·a_1_0·b_5_19 + a_2_32·b_2_52·b_2_6
       + a_2_32·b_2_53 + b_2_6·a_1_03·b_5_19 + a_2_32·a_1_0·b_5_19 + a_2_33·b_2_62
  27. a_1_0·b_9_44 + b_2_62·a_1_0·b_5_19 + b_2_5·b_2_6·a_1_0·b_5_19 + a_2_3·b_2_64
       + a_2_3·b_2_52·b_2_62 + a_2_3·b_2_5·a_1_0·b_5_19 + a_2_32·b_2_63
       + a_2_32·b_2_52·b_2_6 + a_2_32·b_2_53 + b_2_6·a_1_03·b_5_19 + a_2_33·b_2_62
  28. a_2_3·a_9_29 + a_2_3·b_2_64·a_1_0 + a_2_3·b_2_53·b_2_6·a_1_0 + a_2_3·b_2_54·a_1_0
       + a_2_32·b_2_6·b_5_20 + a_2_32·b_2_6·b_5_19 + a_2_32·b_2_5·b_5_20
       + a_2_32·b_2_52·b_2_6·a_1_0
  29. b_2_62·b_1_22·b_5_20 + b_2_64·b_1_23 + b_2_5·b_9_44 + b_2_5·b_2_62·b_5_20
       + b_2_5·b_2_62·b_5_19 + b_2_52·b_2_6·b_5_20 + b_2_52·b_2_6·b_5_19 + b_2_4·b_9_41
       + b_2_4·b_2_62·b_5_20 + b_2_4·b_2_64·b_1_2 + b_2_42·b_2_6·b_5_20 + b_2_43·b_5_20
       + b_2_44·b_2_6·b_1_2 + b_2_45·b_1_2 + b_2_6·a_9_29 + b_2_65·a_1_0 + b_2_5·a_9_29
       + b_2_4·a_9_29 + a_2_3·b_9_41 + a_2_3·b_2_62·b_5_20 + a_2_3·b_2_62·b_5_19
       + a_2_3·b_2_5·b_2_6·b_5_20 + a_2_3·b_2_5·b_2_6·b_5_19 + a_2_3·b_2_52·b_5_19
       + a_2_3·b_2_43·b_2_6·b_1_2 + a_2_3·b_2_44·b_1_2 + a_1_02·b_9_41
       + a_2_32·b_2_5·b_5_19 + a_2_3·b_2_6·a_1_02·b_5_19 + a_2_32·b_2_53·a_1_0
       + a_2_33·b_5_19
  30. b_2_4·b_9_44 + b_2_4·b_9_41 + b_2_4·b_2_62·b_5_20 + b_2_42·b_2_63·b_1_2
       + b_2_43·b_5_20 + b_2_43·b_2_62·b_1_2 + b_2_44·b_2_6·b_1_2 + b_2_45·b_1_2
       + a_2_3·b_9_41 + a_2_3·b_2_62·b_5_19 + a_2_3·b_2_5·b_2_6·b_5_20
       + a_2_3·b_2_5·b_2_6·b_5_19 + a_2_3·b_2_43·b_2_6·b_1_2 + a_2_3·b_2_44·b_1_2
       + a_2_3·b_2_54·a_1_0 + a_2_32·b_2_5·b_5_20 + a_2_32·b_2_5·b_5_19 + b_2_64·a_1_03
       + a_2_32·b_2_52·b_2_6·a_1_0
  31. b_2_4·a_9_29 + a_2_3·b_9_44 + a_2_3·b_2_62·b_5_20 + a_2_3·b_2_62·b_5_19
       + a_2_3·b_2_5·b_2_6·b_5_20 + a_2_3·b_2_5·b_2_6·b_5_19 + a_2_3·b_2_64·a_1_0
       + a_2_3·b_2_53·b_2_6·a_1_0 + a_2_32·b_2_6·b_5_20 + a_2_32·b_2_6·b_5_19
       + a_2_32·b_2_5·b_5_19 + a_2_3·b_2_6·a_1_02·b_5_19 + a_2_32·b_2_52·b_2_6·a_1_0
       + a_2_32·b_2_53·a_1_0
  32. b_1_26·b_5_20 + b_2_62·b_1_27 + b_2_4·b_2_62·b_5_20 + b_2_4·b_2_64·b_1_2
       + b_2_42·b_2_6·b_5_20 + b_2_42·b_2_63·b_1_2 + b_2_43·b_2_62·b_1_2
       + b_2_44·b_2_6·b_1_2 + b_2_45·b_1_2 + b_1_22·a_9_29 + a_10_39·b_1_2
       + b_2_6·a_1_1·b_1_28 + b_2_4·a_9_29 + a_2_3·b_2_62·b_5_20 + a_2_3·b_2_64·a_1_0
       + a_2_3·b_2_53·b_2_6·a_1_0 + a_2_3·b_2_54·a_1_0 + a_2_32·b_2_6·b_5_19
       + a_2_32·b_2_5·b_5_20 + b_2_64·a_1_03 + a_2_3·b_2_6·a_1_02·b_5_19
  33. b_2_4·a_9_29 + a_2_3·b_9_41 + a_2_3·b_2_62·b_5_20 + a_2_3·b_2_62·b_5_19
       + a_2_3·b_2_5·b_2_6·b_5_20 + a_2_3·b_2_5·b_2_6·b_5_19 + a_2_3·b_2_52·b_5_19
       + a_10_39·a_1_1 + b_2_62·a_1_02·b_5_19 + a_2_3·b_2_64·a_1_0 + a_2_32·b_2_6·b_5_20
       + a_2_32·b_2_52·b_2_6·a_1_0
  34. b_2_4·a_9_29 + a_2_3·b_9_41 + a_2_3·b_2_62·b_5_20 + a_2_3·b_2_62·b_5_19
       + a_2_3·b_2_5·b_2_6·b_5_20 + a_2_3·b_2_5·b_2_6·b_5_19 + a_2_3·b_2_52·b_5_19
       + a_10_39·a_1_0 + b_2_62·a_1_02·b_5_19 + a_2_3·b_2_64·a_1_0 + a_2_32·b_2_6·b_5_20
       + a_2_32·b_2_52·b_2_6·a_1_0
  35. b_1_22·b_9_41 + b_1_26·b_5_20 + b_10_53·b_1_2 + b_2_65·b_1_2 + b_2_4·b_9_41
       + b_2_42·b_2_63·b_1_2 + b_2_43·b_5_20 + b_2_44·b_2_6·b_1_2 + b_2_45·b_1_2
       + b_1_22·a_9_29 + a_1_1·b_1_2·b_9_41 + b_2_54·b_2_6·a_1_1 + b_2_54·b_2_6·a_1_0
       + a_2_3·b_9_41
  36. a_1_1·b_1_2·b_9_41 + b_10_53·a_1_1 + b_2_65·a_1_0 + b_2_54·b_2_6·a_1_0 + b_2_4·a_9_29
       + a_2_3·b_2_52·b_5_20 + a_2_3·b_2_43·b_2_6·b_1_2 + a_2_3·b_2_53·b_2_6·a_1_0
       + a_2_3·b_2_54·a_1_0 + a_2_32·b_2_6·b_5_19 + b_2_64·a_1_03
       + a_2_3·b_2_6·a_1_02·b_5_19 + a_2_32·b_2_53·a_1_0
  37. b_10_53·a_1_0 + b_2_65·a_1_0 + b_2_54·b_2_6·a_1_0 + a_2_3·b_2_52·b_5_20
       + a_2_3·b_2_44·b_1_2 + a_2_3·b_2_64·a_1_0 + a_2_32·b_2_6·b_5_20
       + a_2_32·b_2_5·b_5_20 + b_2_64·a_1_03 + a_2_3·b_2_6·a_1_02·b_5_19
       + a_2_32·b_2_53·a_1_0
  38. b_2_4·b_2_62·b_1_2·b_5_20 + b_2_42·b_2_6·b_1_2·b_5_20 + b_2_42·b_2_64
       + b_2_43·b_1_2·b_5_20 + b_2_43·b_2_63 + b_2_45·b_2_6 + b_2_46 + b_2_5·a_1_0·b_9_41
       + b_2_53·a_1_0·b_5_19 + b_2_4·a_10_39 + a_2_3·b_5_19·b_5_20 + a_2_3·b_2_5·b_2_64
       + a_2_3·b_2_53·b_2_62 + a_2_3·b_2_44·b_2_6 + a_2_3·b_2_5·b_2_6·a_1_0·b_5_19
       + a_2_32·b_2_64 + a_2_32·b_2_5·b_2_63 + a_2_32·b_2_54 + a_10_39·a_1_02
       + a_2_32·b_2_6·a_1_0·b_5_19 + a_2_33·b_2_5·b_2_62 + a_2_33·b_2_53
  39. b_2_5·a_1_0·b_9_41 + b_2_53·a_1_0·b_5_19 + a_2_3·b_5_19·b_5_20 + a_2_3·b_2_5·b_2_64
       + a_2_3·b_2_53·b_2_62 + a_2_3·b_2_44·b_2_6 + a_2_3·a_10_39
       + a_2_3·b_2_5·b_2_6·a_1_0·b_5_19 + a_2_32·b_2_5·b_2_63 + a_2_32·b_2_54
       + a_10_39·a_1_02 + b_2_62·a_1_03·b_5_19 + a_2_3·b_2_64·a_1_02 + a_2_33·b_2_63
       + a_2_33·b_2_53
  40. b_2_4·b_10_53 + b_2_4·b_2_65 + b_2_43·b_2_63 + b_2_45·b_2_6 + b_2_46
       + b_2_6·a_1_1·b_9_41 + b_2_6·a_1_0·b_9_41 + a_2_3·b_2_53·b_2_62 + a_2_3·b_2_45
       + a_2_32·b_2_64 + a_2_32·b_2_5·b_2_63 + a_2_32·b_2_52·b_2_62
       + a_2_32·b_2_53·b_2_6 + a_2_3·b_2_64·a_1_02 + a_2_32·b_2_5·a_1_0·b_5_19
       + a_2_33·b_2_63 + a_2_33·b_2_5·b_2_62 + a_2_33·b_2_52·b_2_6 + a_2_33·b_2_53
  41. a_2_3·b_10_53 + a_2_3·b_2_65 + a_2_3·b_2_53·b_2_62 + a_2_3·b_2_44·b_2_6
       + a_2_3·b_2_45 + a_2_32·b_2_64 + a_2_32·b_2_5·b_2_63 + a_2_32·b_2_52·b_2_62
       + a_2_32·b_2_53·b_2_6 + a_2_3·b_2_64·a_1_02 + a_2_32·b_2_6·a_1_0·b_5_19
       + a_2_33·b_2_63 + a_2_33·b_2_52·b_2_6 + a_2_33·b_2_53
  42. b_2_5·b_2_6·b_9_44 + b_2_5·b_2_63·b_5_20 + b_2_5·b_2_63·b_5_19
       + b_2_52·b_2_62·b_5_20 + b_2_52·b_2_62·b_5_19 + b_2_4·b_2_6·b_9_41
       + b_2_42·b_2_64·b_1_2 + b_2_43·b_2_63·b_1_2 + b_2_44·b_5_20
       + b_2_44·b_2_62·b_1_2 + b_2_46·b_1_2 + b_2_55·b_2_6·a_1_0 + b_2_4·a_10_39·b_1_2
       + a_2_3·b_2_6·b_9_41 + a_2_3·b_2_52·b_2_6·b_5_20 + a_2_3·b_2_52·b_2_6·b_5_19
       + a_2_3·b_2_45·b_1_2 + b_2_6·a_1_02·b_9_41 + a_2_3·b_2_54·b_2_6·a_1_0
       + a_2_32·b_2_62·b_5_19 + a_2_32·b_2_5·b_2_6·b_5_19 + a_2_3·a_10_39·a_1_0
       + a_2_3·b_2_62·a_1_02·b_5_19 + a_2_33·b_2_6·b_5_19 + a_2_33·b_2_5·b_5_19
  43. b_5_20·a_9_29 + b_2_62·b_1_2·a_9_29 + a_2_3·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_66
       + a_2_3·b_2_52·b_2_64 + a_2_3·b_2_54·b_2_62 + a_2_3·b_2_55·b_2_6
       + a_2_3·b_2_4·b_1_2·b_9_41 + a_2_3·b_2_45·b_2_6 + a_2_32·b_2_54·b_2_6
       + b_2_63·a_1_03·b_5_19 + a_2_3·b_2_65·a_1_02 + a_2_32·a_10_39
       + a_2_32·b_2_52·a_1_0·b_5_19 + a_2_33·b_2_52·b_2_62 + a_2_33·b_2_53·b_2_6
  44. b_2_52·b_10_53 + b_2_52·b_2_65 + b_2_55·b_2_62 + b_2_44·b_2_63
       + b_2_45·b_2_62 + b_2_46·b_2_6 + b_2_47 + b_5_19·a_9_29 + b_2_6·b_1_23·a_9_29
       + b_2_62·b_1_2·a_9_29 + b_2_64·a_1_0·b_5_19 + b_2_53·b_2_6·a_1_0·b_5_19
       + b_2_54·a_1_0·b_5_19 + a_2_3·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_6·b_1_2·b_9_41
       + a_2_3·b_2_5·b_5_19·b_5_20 + a_2_3·b_2_5·b_2_65 + a_2_3·b_2_52·b_2_64
       + a_2_3·b_2_53·b_2_63 + a_2_3·b_2_55·b_2_6 + a_2_3·b_2_46
       + a_2_3·b_2_52·b_2_6·a_1_0·b_5_19 + a_2_32·b_2_65 + a_2_32·b_2_53·b_2_62
       + a_2_32·b_2_54·b_2_6 + a_2_32·b_2_55 + b_2_6·a_10_39·a_1_02
       + a_2_33·b_2_53·b_2_6 + a_2_33·b_2_54
  45. b_5_20·b_9_44 + b_5_20·b_9_41 + b_2_63·b_1_28 + b_2_64·b_1_2·b_5_20
       + b_2_66·b_1_22 + b_2_52·b_5_19·b_5_20 + b_2_4·b_2_66 + b_2_42·b_2_65
       + b_2_43·b_2_64 + b_2_44·b_1_2·b_5_20 + b_2_47 + b_5_20·a_9_29
       + b_2_6·b_10_53·a_1_1·b_1_2 + b_2_6·a_10_39·b_1_22 + b_2_62·b_1_2·a_9_29
       + b_2_62·a_10_39 + b_2_64·a_1_0·b_5_19 + b_2_5·b_2_6·a_10_39
       + b_2_53·b_2_6·a_1_1·b_5_19 + a_2_3·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_52·b_2_64
       + a_2_3·b_2_53·b_2_63 + a_2_3·b_2_55·b_2_6 + a_2_3·b_2_45·b_2_6 + a_2_3·b_2_46
       + a_2_3·b_2_6·a_10_39 + a_2_3·b_2_63·a_1_0·b_5_19 + a_2_32·b_2_5·b_2_64
       + a_2_32·b_2_52·b_2_63 + a_2_32·b_2_53·b_2_62 + b_2_6·a_10_39·a_1_02
       + b_2_63·a_1_03·b_5_19 + a_2_3·b_2_65·a_1_02 + a_2_32·b_2_5·b_2_6·a_1_0·b_5_19
       + a_2_32·b_2_52·a_1_0·b_5_19 + a_2_33·b_2_52·b_2_62 + a_2_33·b_2_53·b_2_6
       + a_2_33·b_2_54
  46. b_5_20·b_9_44 + b_5_20·b_9_41 + b_5_19·b_9_44 + b_2_6·b_10_53·b_1_22
       + b_2_62·b_5_19·b_5_20 + b_2_62·b_1_210 + b_2_62·b_10_53 + b_2_63·b_1_28
       + b_2_64·b_1_2·b_5_20 + b_2_64·b_1_26 + b_2_65·b_1_24 + b_2_66·b_1_22
       + b_2_67 + b_2_5·b_2_6·b_5_19·b_5_20 + b_2_5·b_2_66 + b_2_52·b_5_19·b_5_20
       + b_2_52·b_2_65 + b_2_53·b_2_64 + b_2_54·b_2_63 + b_2_55·b_2_62
       + b_2_4·b_2_6·b_1_2·b_9_41 + b_2_4·b_2_66 + b_2_45·b_2_62 + b_2_46·b_2_6
       + b_5_20·a_9_29 + b_5_19·a_9_29 + b_2_6·b_1_23·a_9_29 + b_2_62·a_1_0·b_9_41
       + b_2_62·a_10_39 + b_2_64·a_1_0·b_5_19 + b_2_5·b_2_6·a_10_39
       + b_2_53·b_2_6·a_1_1·b_5_19 + b_2_53·b_2_6·a_1_0·b_5_19 + b_2_4·b_2_6·a_10_39
       + b_2_42·a_10_39 + a_2_3·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_6·b_1_2·b_9_41
       + a_2_3·b_2_66 + a_2_3·b_2_5·b_5_19·b_5_20 + a_2_3·b_2_5·b_2_65
       + a_2_3·b_2_52·b_2_64 + a_2_3·b_2_53·b_2_63 + a_2_3·b_2_54·b_2_62
       + a_2_3·b_2_4·b_1_2·b_9_41 + a_2_3·b_2_46 + a_2_3·b_2_6·a_10_39 + a_2_32·b_2_65
       + a_2_32·b_2_52·b_2_63 + b_2_6·a_10_39·a_1_02 + b_2_63·a_1_03·b_5_19
       + a_2_3·b_2_65·a_1_02 + a_2_32·b_2_5·b_2_6·a_1_0·b_5_19
       + a_2_32·b_2_52·a_1_0·b_5_19 + a_2_33·b_2_54
  47. b_2_5·b_2_62·b_9_41 + b_2_5·b_2_64·b_5_20 + b_2_5·b_2_64·b_5_19
       + b_2_52·b_2_6·b_9_41 + b_2_53·b_2_62·b_5_20 + b_2_54·b_2_6·b_5_19
       + b_2_4·b_2_62·b_9_41 + b_2_4·b_2_66·b_1_2 + b_2_42·b_2_6·b_9_41
       + b_2_42·b_2_65·b_1_2 + b_2_45·b_5_20 + b_2_45·b_2_62·b_1_2 + b_2_47·b_1_2
       + a_10_39·b_5_20 + b_2_6·b_1_24·a_9_29 + b_2_6·b_10_53·a_1_1·b_1_22
       + b_2_62·b_1_22·a_9_29 + b_2_4·b_2_6·a_10_39·b_1_2 + a_2_3·b_2_64·b_5_20
       + a_2_3·b_2_5·b_2_63·b_5_20 + a_2_3·b_2_5·b_2_63·b_5_19
       + a_2_3·b_2_52·b_2_62·b_5_20 + a_2_3·b_2_54·b_5_20 + a_2_3·b_2_4·b_2_6·b_9_41
       + a_2_3·b_2_45·b_2_6·b_1_2 + b_2_64·a_1_02·b_5_19 + a_2_3·b_2_66·a_1_0
       + a_2_3·b_2_55·b_2_6·a_1_0 + a_2_32·b_2_5·b_2_62·b_5_20
       + a_2_32·b_2_5·b_2_62·b_5_19 + a_2_32·b_2_53·b_5_20 + a_2_3·b_2_6·a_10_39·a_1_0
       + a_2_32·b_2_55·a_1_0 + a_2_33·b_2_62·b_5_19 + a_2_33·b_2_5·b_2_6·b_5_19
  48. b_10_53·b_5_19 + b_2_6·b_10_53·b_1_23 + b_2_62·b_10_53·b_1_2 + b_2_65·b_5_19
       + b_2_66·b_1_23 + b_2_67·b_1_2 + b_2_5·b_2_62·b_9_41 + b_2_5·b_2_64·b_5_20
       + b_2_5·b_2_64·b_5_19 + b_2_52·b_2_6·b_9_41 + b_2_53·b_2_62·b_5_20
       + b_2_53·b_2_62·b_5_19 + b_2_54·b_2_6·b_5_19 + b_2_4·b_2_62·b_9_41
       + b_2_4·b_2_66·b_1_2 + b_2_42·b_2_6·b_9_41 + b_2_45·b_5_20 + b_2_47·b_1_2
       + a_10_39·b_5_20 + b_2_6·b_1_24·a_9_29 + b_2_62·b_1_22·a_9_29 + b_2_56·b_2_6·a_1_1
       + b_2_56·b_2_6·a_1_0 + b_2_4·b_2_6·a_10_39·b_1_2 + a_2_3·b_2_64·b_5_20
       + a_2_3·b_2_64·b_5_19 + a_2_3·b_2_5·b_2_63·b_5_20 + a_2_3·b_2_52·b_2_62·b_5_20
       + a_2_3·b_2_52·b_2_62·b_5_19 + a_2_3·b_2_53·b_2_6·b_5_19 + a_2_3·b_2_54·b_5_20
       + a_2_3·b_2_4·b_2_6·b_9_41 + a_2_3·b_2_45·b_2_6·b_1_2 + a_2_3·b_2_46·b_1_2
       + b_2_62·a_1_02·b_9_41 + a_2_3·b_2_66·a_1_0 + a_2_3·b_2_55·b_2_6·a_1_0
       + a_2_32·b_2_5·b_2_62·b_5_19 + a_2_32·b_2_52·b_2_6·b_5_19
       + a_2_32·b_2_53·b_5_20 + a_2_32·b_2_53·b_5_19 + a_2_3·b_2_5·a_10_39·a_1_0
       + a_2_33·b_2_62·b_5_19
  49. b_2_5·b_10_53·b_5_20 + b_2_5·b_2_65·b_5_20 + b_2_54·b_2_62·b_5_20
       + b_2_43·b_2_65·b_1_2 + b_2_44·b_2_64·b_1_2 + b_2_46·b_5_20
       + b_2_46·b_2_62·b_1_2 + b_2_47·b_2_6·b_1_2 + b_2_42·b_2_6·a_10_39·b_1_2
       + a_2_3·b_2_5·b_2_64·b_5_20 + a_2_3·b_2_52·b_2_63·b_5_20
       + a_2_3·b_2_53·b_2_62·b_5_20 + a_2_3·b_2_54·b_2_6·b_5_20
       + a_2_3·b_2_42·b_2_6·b_9_41 + a_2_3·b_2_46·b_2_6·b_1_2 + a_2_3·b_2_47·b_1_2
       + a_2_32·b_2_64·b_5_19 + a_2_32·b_2_5·b_2_63·b_5_20
       + a_2_32·b_2_5·b_2_63·b_5_19 + a_2_32·b_2_52·b_2_62·b_5_20
       + a_2_32·b_2_53·b_2_6·b_5_20 + a_2_32·b_2_54·b_5_20 + a_10_39·a_1_02·b_5_19
       + a_2_33·b_2_63·b_5_19 + a_2_33·b_2_5·b_2_62·b_5_19
       + a_2_33·b_2_52·b_2_6·b_5_19 + b_2_62·a_10_39·a_1_03
  50. a_9_292 + b_2_68·a_1_02 + a_2_32·b_2_54·b_2_63 + a_2_32·b_2_57
       + a_2_32·b_2_53·b_2_6·a_1_0·b_5_19 + a_2_33·b_2_54·b_2_62 + a_2_33·b_2_56
  51. a_9_29·b_9_44 + a_9_29·b_9_41 + b_2_6·b_10_53·a_1_1·b_1_25
       + b_2_62·a_10_39·b_1_24 + b_2_63·b_1_23·a_9_29 + b_2_63·a_10_39·b_1_22
       + b_2_64·a_1_0·b_9_41 + b_2_66·a_1_0·b_5_19 + b_2_52·b_5_19·a_9_29
       + b_2_4·b_2_63·a_10_39 + b_2_42·b_2_62·a_10_39 + a_2_3·b_2_63·b_5_19·b_5_20
       + a_2_3·b_2_68 + a_2_3·b_2_52·b_2_66 + a_2_3·b_2_47·b_2_6
       + b_2_6·a_10_39·a_1_0·b_5_19 + a_2_3·b_2_53·a_10_39 + a_2_3·b_2_55·a_1_0·b_5_19
       + a_2_32·b_2_5·b_2_6·b_5_19·b_5_20 + a_2_32·b_2_5·b_2_66
       + a_2_32·b_2_52·b_5_19·b_5_20 + a_2_32·b_2_53·b_2_64 + a_2_32·b_2_54·b_2_63
       + a_2_32·b_2_55·b_2_62 + a_2_32·b_2_56·b_2_6 + a_2_32·b_2_62·a_10_39
       + a_2_32·b_2_52·a_10_39 + a_2_33·b_2_53·b_2_63 + a_2_33·b_2_54·b_2_62
       + a_2_33·b_2_55·b_2_6 + a_2_33·b_2_56
  52. b_9_442 + b_9_41·b_9_44 + b_2_6·b_10_53·b_1_26 + b_2_62·b_5_20·b_9_41
       + b_2_62·b_5_19·b_9_41 + b_2_62·b_1_214 + b_2_63·b_1_212
       + b_2_63·b_10_53·b_1_22 + b_2_65·b_1_28 + b_2_66·b_1_26 + b_2_68·b_1_22
       + b_2_5·b_2_6·b_5_19·b_9_41 + b_2_5·b_2_63·b_5_19·b_5_20
       + b_2_52·b_2_62·b_5_19·b_5_20 + b_2_52·b_2_67 + b_2_53·b_2_6·b_5_19·b_5_20
       + b_2_56·b_2_63 + b_2_4·b_2_68 + b_2_42·b_5_20·b_9_41 + b_2_42·b_2_67
       + b_2_43·b_2_6·b_1_2·b_9_41 + b_2_43·b_2_66 + b_2_44·b_1_2·b_9_41
       + b_2_45·b_2_64 + b_2_48·b_2_6 + a_9_29·b_9_44 + b_2_6·a_10_39·b_1_26
       + b_2_62·a_10_39·b_1_24 + b_2_63·b_1_23·a_9_29 + b_2_64·a_1_0·b_9_41
       + b_2_5·b_2_6·b_5_19·a_9_29 + b_2_5·b_2_63·a_10_39 + b_2_52·b_5_19·a_9_29
       + b_2_52·b_2_62·a_10_39 + b_2_55·b_2_6·a_1_1·b_5_19 + b_2_55·b_2_6·a_1_0·b_5_19
       + b_2_4·b_2_63·a_10_39 + b_2_42·b_2_62·a_10_39 + b_2_43·b_2_6·a_10_39
       + a_2_3·b_2_68 + a_2_3·b_2_5·b_2_62·b_5_19·b_5_20 + a_2_3·b_2_5·b_2_67
       + a_2_3·b_2_52·b_2_66 + a_2_3·b_2_54·b_2_64 + a_2_3·b_2_55·b_2_63
       + a_2_3·b_2_56·b_2_62 + a_2_3·b_2_57·b_2_6 + a_2_3·b_2_42·b_2_6·b_1_2·b_9_41
       + a_2_3·b_2_43·b_1_2·b_9_41 + b_2_5·a_10_39·a_1_0·b_5_19 + a_2_3·b_2_63·a_10_39
       + a_2_3·b_2_65·a_1_0·b_5_19 + a_2_3·b_2_5·b_2_62·a_10_39
       + a_2_3·b_2_52·b_2_6·a_10_39 + a_2_3·b_2_53·a_10_39
       + a_2_3·b_2_54·b_2_6·a_1_0·b_5_19 + a_2_32·b_2_52·b_5_19·b_5_20
       + a_2_32·b_2_52·b_2_65 + a_2_32·b_2_54·b_2_63 + a_2_32·b_2_55·b_2_62
       + a_2_32·b_2_56·b_2_6 + a_2_32·b_2_57 + b_2_63·a_10_39·a_1_02
       + b_2_65·a_1_03·b_5_19 + a_2_3·a_10_39·a_1_0·b_5_19 + a_2_32·b_2_52·a_10_39
       + a_2_33·b_2_53·b_2_63 + a_2_33·b_2_56
  53. b_9_442 + b_10_53·b_1_28 + b_2_6·b_10_53·b_1_2·b_5_20 + b_2_6·b_10_53·b_1_26
       + b_2_62·b_1_214 + b_2_62·b_10_53·b_1_24 + b_2_65·b_1_28
       + b_2_66·b_1_2·b_5_20 + b_2_53·b_2_66 + b_2_54·b_2_65 + b_2_55·b_2_64
       + b_2_56·b_2_63 + b_2_4·b_2_6·b_5_20·b_9_41 + b_2_4·b_2_68 + b_2_42·b_2_67
       + b_2_43·b_2_66 + b_2_44·b_2_65 + b_2_46·b_1_2·b_5_20 + b_2_49
       + a_10_39·b_1_28 + b_2_62·a_10_39·b_1_24 + b_2_63·a_10_39·b_1_22
       + b_2_64·a_1_0·b_9_41 + b_2_66·a_1_0·b_5_19 + b_2_55·b_2_6·a_1_1·b_5_19
       + b_2_55·b_2_6·a_1_0·b_5_19 + b_2_4·b_2_63·a_10_39 + b_2_43·b_2_6·a_10_39
       + b_2_44·a_10_39 + a_2_3·b_2_5·b_2_67 + a_2_3·b_2_53·b_2_65
       + a_2_3·b_2_54·b_2_64 + a_2_3·b_2_42·b_2_6·b_1_2·b_9_41 + a_2_3·b_2_47·b_2_6
       + a_2_3·b_2_65·a_1_0·b_5_19 + a_2_32·b_2_62·b_5_19·b_5_20 + a_2_32·b_2_67
       + a_2_32·b_2_5·b_2_6·b_5_19·b_5_20 + a_2_32·b_2_54·b_2_63
       + a_2_32·b_2_56·b_2_6 + a_2_32·b_2_57 + a_2_3·b_2_67·a_1_02
       + a_2_32·b_2_53·b_2_6·a_1_0·b_5_19 + a_2_33·b_2_56 + c_16_113·b_1_22
  54. b_9_442 + b_9_41·b_9_44 + b_2_6·b_10_53·b_1_2·b_5_20 + b_2_6·b_10_53·b_1_26
       + b_2_62·b_5_20·b_9_41 + b_2_62·b_5_19·b_9_41 + b_2_62·b_1_214 + b_2_63·b_1_212
       + b_2_65·b_1_28 + b_2_66·b_1_2·b_5_20 + b_2_66·b_1_26
       + b_2_5·b_2_6·b_5_19·b_9_41 + b_2_5·b_2_63·b_5_19·b_5_20
       + b_2_52·b_2_62·b_5_19·b_5_20 + b_2_52·b_2_67 + b_2_53·b_2_6·b_5_19·b_5_20
       + b_2_56·b_2_63 + b_2_4·b_2_68 + b_2_42·b_5_20·b_9_41 + b_2_42·b_2_67
       + b_2_43·b_2_6·b_1_2·b_9_41 + b_2_43·b_2_66 + b_2_44·b_1_2·b_9_41
       + b_2_45·b_2_6·b_1_2·b_5_20 + b_2_46·b_1_2·b_5_20 + b_2_46·b_2_63 + b_2_48·b_2_6
       + b_2_49 + b_10_53·a_1_1·b_1_27 + b_2_6·a_10_39·b_1_26 + b_2_63·b_1_23·a_9_29
       + b_2_64·a_1_0·b_9_41 + b_2_66·a_1_0·b_5_19 + b_2_5·b_2_6·b_5_19·a_9_29
       + b_2_5·b_2_63·a_10_39 + b_2_52·b_5_19·a_9_29 + b_2_52·b_2_62·a_10_39
       + b_2_55·b_2_6·a_1_1·b_5_19 + b_2_4·b_2_63·a_10_39 + b_2_42·b_2_62·a_10_39
       + b_2_44·a_10_39 + a_2_3·b_2_63·b_5_19·b_5_20 + a_2_3·b_2_5·b_2_62·b_5_19·b_5_20
       + a_2_3·b_2_5·b_2_67 + a_2_3·b_2_52·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_52·b_2_66
       + a_2_3·b_2_53·b_2_65 + a_2_3·b_2_54·b_2_64 + a_2_3·b_2_57·b_2_6
       + a_2_3·b_2_42·b_2_6·b_1_2·b_9_41 + a_2_3·b_2_43·b_1_2·b_9_41 + a_2_3·b_2_47·b_2_6
       + b_2_5·a_10_39·a_1_0·b_5_19 + a_2_3·b_2_63·a_10_39 + a_2_3·b_2_5·b_2_62·a_10_39
       + a_2_3·b_2_52·b_2_6·a_10_39 + a_2_3·b_2_53·a_10_39
       + a_2_3·b_2_54·b_2_6·a_1_0·b_5_19 + a_2_3·b_2_55·a_1_0·b_5_19
       + a_2_32·b_2_62·b_5_19·b_5_20 + a_2_32·b_2_67
       + a_2_32·b_2_5·b_2_6·b_5_19·b_5_20 + a_2_32·b_2_52·b_2_65
       + a_2_32·b_2_53·b_2_64 + a_2_32·b_2_54·b_2_63 + a_2_32·b_2_5·b_2_6·a_10_39
       + a_2_32·b_2_52·a_10_39 + a_2_33·b_2_53·b_2_63 + a_2_33·b_2_54·b_2_62
       + a_2_33·b_2_56 + c_16_113·a_1_1·b_1_2
  55. b_9_442 + b_9_412 + b_2_62·b_1_214 + b_2_55·b_2_64 + b_2_58·b_2_6
       + b_2_4·b_2_68 + b_2_43·b_2_66 + b_2_48·b_2_6 + b_2_64·a_1_0·b_9_41
       + b_2_66·a_1_0·b_5_19 + b_2_56·a_1_0·b_5_19 + a_2_3·b_2_63·b_5_19·b_5_20
       + a_2_3·b_2_52·b_2_66 + a_2_3·b_2_54·b_2_64 + a_2_3·b_2_56·b_2_62
       + a_2_3·b_2_65·a_1_0·b_5_19 + a_2_3·b_2_5·b_2_62·a_10_39 + a_2_3·b_2_53·a_10_39
       + a_2_3·b_2_54·b_2_6·a_1_0·b_5_19 + a_2_3·b_2_55·a_1_0·b_5_19
       + a_2_32·b_2_62·b_5_19·b_5_20 + a_2_32·b_2_5·b_2_6·b_5_19·b_5_20
       + a_2_32·b_2_55·b_2_62 + b_2_63·a_10_39·a_1_02 + a_2_32·b_2_52·a_10_39
       + a_2_32·b_2_54·a_1_0·b_5_19 + a_2_33·b_2_53·b_2_63 + a_2_33·b_2_54·b_2_62
       + c_16_113·a_1_02
  56. a_10_39·a_9_29 + b_2_64·a_10_39·a_1_0 + b_2_53·b_2_6·a_10_39·a_1_0
       + b_2_54·a_10_39·a_1_0 + a_2_3·b_2_6·a_10_39·b_5_20 + a_2_3·b_2_6·a_10_39·b_5_19
       + a_2_3·b_2_5·a_10_39·b_5_20 + a_2_3·b_2_52·b_2_6·a_10_39·a_1_0
       + a_2_32·a_10_39·b_5_20 + a_2_33·b_2_5·b_2_63·b_5_19
       + a_2_33·b_2_53·b_2_6·b_5_19
  57. b_10_53·b_1_24·b_5_20 + b_2_62·b_1_2·b_5_20·b_9_41 + b_2_62·b_10_53·b_5_20
       + b_2_62·b_10_53·b_1_25 + b_2_66·b_1_27 + b_2_67·b_5_20 + b_2_53·b_2_64·b_5_20
       + b_2_4·b_2_6·b_1_2·b_5_20·b_9_41 + b_2_4·b_2_64·b_9_41
       + b_2_42·b_1_2·b_5_20·b_9_41 + b_2_42·b_2_63·b_9_41 + b_2_42·b_2_67·b_1_2
       + b_2_44·b_2_6·b_9_41 + b_2_44·b_2_65·b_1_2 + b_2_45·b_9_41 + b_2_46·b_2_6·b_5_20
       + b_2_46·b_2_63·b_1_2 + b_2_47·b_2_62·b_1_2 + b_2_49·b_1_2 + b_10_53·a_9_29
       + a_10_39·b_9_44 + b_2_6·b_10_53·a_1_1·b_1_26 + b_2_6·a_10_39·b_1_27
       + b_2_62·a_10_39·b_5_20 + b_2_62·a_10_39·b_5_19 + b_2_62·a_10_39·b_1_25
       + b_2_63·a_10_39·b_1_23 + b_2_65·a_9_29 + b_2_5·b_2_6·a_10_39·b_5_20
       + b_2_5·b_2_6·a_10_39·b_5_19 + b_2_54·b_2_6·a_9_29 + b_2_42·b_2_62·a_10_39·b_1_2
       + b_2_44·a_10_39·b_1_2 + a_2_3·b_2_66·b_5_19 + a_2_3·b_2_5·b_2_65·b_5_19
       + a_2_3·b_2_52·b_2_64·b_5_19 + a_2_3·b_2_53·b_2_63·b_5_19
       + a_2_3·b_2_54·b_2_62·b_5_19 + a_2_3·b_2_56·b_5_20 + a_2_3·b_2_43·b_2_6·b_9_41
       + a_2_3·b_2_44·b_9_41 + a_2_3·b_2_48·b_1_2 + b_2_64·a_1_02·b_9_41
       + b_2_64·a_10_39·a_1_0 + b_2_66·a_1_02·b_5_19 + b_2_54·a_10_39·a_1_0
       + a_2_3·b_2_5·a_10_39·b_5_20 + a_2_3·b_2_5·a_10_39·b_5_19 + a_2_3·b_2_57·b_2_6·a_1_0
       + a_2_32·b_2_65·b_5_19 + a_2_32·b_2_5·b_2_64·b_5_20
       + a_2_32·b_2_5·b_2_64·b_5_19 + a_2_32·b_2_53·b_2_62·b_5_19 + b_2_68·a_1_03
       + a_2_3·b_2_63·a_10_39·a_1_0 + a_2_3·b_2_52·b_2_6·a_10_39·a_1_0
       + a_2_32·a_10_39·b_5_20 + a_2_32·b_2_57·a_1_0 + a_2_33·b_2_5·b_2_63·b_5_19
       + a_2_33·b_2_53·b_2_6·b_5_19 + a_2_33·b_2_54·b_5_19
  58. b_10_53·b_9_44 + b_10_53·b_9_41 + b_10_53·b_1_24·b_5_20 + b_2_6·b_10_53·b_1_27
       + b_2_62·b_1_2·b_5_20·b_9_41 + b_2_62·b_10_53·b_1_25 + b_2_64·b_10_53·b_1_2
       + b_2_65·b_9_44 + b_2_65·b_9_41 + b_2_69·b_1_2 + b_2_54·b_2_6·b_9_41
       + b_2_54·b_2_63·b_5_20 + b_2_54·b_2_63·b_5_19 + b_2_55·b_2_62·b_5_20
       + b_2_56·b_2_6·b_5_19 + b_2_4·b_2_6·b_1_2·b_5_20·b_9_41 + b_2_4·b_2_64·b_9_41
       + b_2_42·b_1_2·b_5_20·b_9_41 + b_2_42·b_2_63·b_9_41 + b_2_44·b_2_65·b_1_2
       + b_2_45·b_9_41 + b_2_45·b_2_64·b_1_2 + b_2_47·b_2_62·b_1_2 + b_2_48·b_2_6·b_1_2
       + b_2_49·b_1_2 + a_10_39·b_9_44 + b_2_6·b_10_53·a_1_1·b_1_26
       + b_2_6·a_10_39·b_1_27 + b_2_62·a_10_39·b_5_20 + b_2_62·a_10_39·b_5_19
       + b_2_62·a_10_39·b_1_25 + b_2_63·a_10_39·b_1_23 + b_2_5·b_2_6·a_10_39·b_5_20
       + b_2_5·b_2_6·a_10_39·b_5_19 + b_2_52·a_10_39·b_5_20 + b_2_58·b_2_6·a_1_1
       + b_2_42·b_2_62·a_10_39·b_1_2 + b_2_43·b_2_6·a_10_39·b_1_2 + b_2_44·a_10_39·b_1_2
       + a_2_3·b_2_66·b_5_20 + a_2_3·b_2_66·b_5_19 + a_2_3·b_2_5·b_2_65·b_5_20
       + a_2_3·b_2_5·b_2_65·b_5_19 + a_2_3·b_2_52·b_2_64·b_5_19
       + a_2_3·b_2_53·b_2_63·b_5_19 + a_2_3·b_2_54·b_2_62·b_5_19
       + a_2_3·b_2_55·b_2_6·b_5_19 + a_2_3·b_2_44·b_9_41 + a_2_3·b_2_47·b_2_6·b_1_2
       + b_2_64·a_1_02·b_9_41 + b_2_66·a_1_02·b_5_19 + b_2_54·a_10_39·a_1_0
       + a_2_3·b_2_6·a_10_39·b_5_20 + a_2_3·b_2_68·a_1_0 + a_2_3·b_2_5·a_10_39·b_5_19
       + a_2_3·b_2_57·b_2_6·a_1_0 + a_2_32·b_2_65·b_5_20 + a_2_32·b_2_65·b_5_19
       + a_2_32·b_2_53·b_2_62·b_5_20 + a_2_32·b_2_55·b_5_20 + a_2_32·b_2_55·b_5_19
       + a_2_3·b_2_63·a_10_39·a_1_0 + a_2_3·b_2_52·b_2_6·a_10_39·a_1_0
       + a_2_3·b_2_53·a_10_39·a_1_0 + a_2_32·a_10_39·b_5_20 + a_2_32·b_2_56·b_2_6·a_1_0
       + a_2_33·b_2_5·b_2_63·b_5_19 + a_2_33·b_2_52·b_2_62·b_5_19
       + a_2_33·b_2_53·b_2_6·b_5_19 + a_2_33·b_2_54·b_5_19
  59. b_10_53·b_9_41 + b_10_53·b_1_29 + b_2_6·b_10_53·b_1_27
       + b_2_62·b_1_2·b_5_20·b_9_41 + b_2_62·b_10_53·b_5_20 + b_2_63·b_10_53·b_1_23
       + b_2_64·b_1_211 + b_2_65·b_9_41 + b_2_65·b_1_29 + b_2_66·b_1_27
       + b_2_67·b_5_20 + b_2_67·b_1_25 + b_2_68·b_1_23 + b_2_53·b_2_64·b_5_19
       + b_2_54·b_2_6·b_9_41 + b_2_55·b_2_62·b_5_20 + b_2_56·b_2_6·b_5_19
       + b_2_4·b_2_6·b_1_2·b_5_20·b_9_41 + b_2_4·b_2_64·b_9_41
       + b_2_42·b_1_2·b_5_20·b_9_41 + b_2_43·b_2_66·b_1_2 + b_2_44·b_2_6·b_9_41
       + b_2_44·b_2_65·b_1_2 + b_2_45·b_2_64·b_1_2 + b_2_46·b_2_6·b_5_20
       + b_2_48·b_2_6·b_1_2 + b_2_49·b_1_2 + b_1_2·a_9_29·b_9_41 + a_10_39·b_9_44
       + a_10_39·b_1_29 + b_2_6·a_10_39·b_1_27 + b_2_62·a_10_39·b_5_20
       + b_2_62·a_10_39·b_5_19 + b_2_63·b_1_24·a_9_29 + b_2_63·a_10_39·b_1_23
       + b_2_64·b_1_22·a_9_29 + b_2_5·b_2_6·a_10_39·b_5_20 + b_2_5·b_2_6·a_10_39·b_5_19
       + b_2_52·a_10_39·b_5_20 + b_2_4·b_2_63·a_10_39·b_1_2
       + b_2_42·b_2_62·a_10_39·b_1_2 + a_2_3·b_2_66·b_5_20 + a_2_3·b_2_5·b_2_65·b_5_19
       + a_2_3·b_2_52·b_2_64·b_5_20 + a_2_3·b_2_52·b_2_64·b_5_19
       + a_2_3·b_2_53·b_2_63·b_5_20 + a_2_3·b_2_53·b_2_63·b_5_19
       + a_2_3·b_2_54·b_2_62·b_5_19 + a_2_3·b_2_55·b_2_6·b_5_19 + a_2_3·b_2_56·b_5_20
       + a_2_3·b_2_44·b_9_41 + a_2_3·b_2_48·b_1_2 + b_2_54·a_10_39·a_1_0
       + a_2_3·b_2_6·a_10_39·b_5_20 + a_2_3·b_2_68·a_1_0 + a_2_3·b_2_5·a_10_39·b_5_19
       + a_2_3·b_2_57·b_2_6·a_1_0 + a_2_32·b_2_65·b_5_20 + a_2_32·b_2_65·b_5_19
       + a_2_32·b_2_5·b_2_64·b_5_19 + a_2_32·b_2_53·b_2_62·b_5_19
       + a_2_32·b_2_55·b_5_19 + b_2_6·a_10_39·a_1_02·b_5_19 + a_2_3·b_2_53·a_10_39·a_1_0
       + a_2_32·b_2_56·b_2_6·a_1_0 + a_2_33·b_2_5·b_2_63·b_5_19
       + b_2_63·a_10_39·a_1_03 + c_16_113·b_1_23 + b_2_4·c_16_113·b_1_2
  60. b_10_53·b_1_24·b_5_20 + b_2_62·b_1_2·b_5_20·b_9_41 + b_2_62·b_10_53·b_5_20
       + b_2_62·b_10_53·b_1_25 + b_2_66·b_1_27 + b_2_67·b_5_20 + b_2_53·b_2_64·b_5_20
       + b_2_4·b_2_6·b_1_2·b_5_20·b_9_41 + b_2_4·b_2_64·b_9_41
       + b_2_42·b_1_2·b_5_20·b_9_41 + b_2_42·b_2_63·b_9_41 + b_2_42·b_2_67·b_1_2
       + b_2_44·b_2_6·b_9_41 + b_2_44·b_2_65·b_1_2 + b_2_45·b_9_41 + b_2_46·b_2_6·b_5_20
       + b_2_46·b_2_63·b_1_2 + b_2_47·b_2_62·b_1_2 + b_2_49·b_1_2 + b_1_2·a_9_29·b_9_41
       + a_10_39·b_9_44 + b_2_6·b_10_53·a_1_1·b_1_26 + b_2_6·a_10_39·b_1_27
       + b_2_62·a_10_39·b_5_20 + b_2_62·a_10_39·b_5_19 + b_2_62·a_10_39·b_1_25
       + b_2_63·b_1_24·a_9_29 + b_2_5·b_2_6·a_10_39·b_5_20 + b_2_5·b_2_6·a_10_39·b_5_19
       + b_2_4·b_2_63·a_10_39·b_1_2 + b_2_42·b_2_62·a_10_39·b_1_2 + b_2_44·a_10_39·b_1_2
       + a_2_3·b_2_66·b_5_19 + a_2_3·b_2_5·b_2_65·b_5_19 + a_2_3·b_2_52·b_2_64·b_5_20
       + a_2_3·b_2_52·b_2_64·b_5_19 + a_2_3·b_2_53·b_2_63·b_5_20
       + a_2_3·b_2_47·b_2_6·b_1_2 + a_2_3·b_2_48·b_1_2 + b_2_64·a_1_02·b_9_41
       + b_2_64·a_10_39·a_1_0 + b_2_66·a_1_02·b_5_19 + b_2_54·a_10_39·a_1_0
       + a_2_3·b_2_68·a_1_0 + a_2_3·b_2_5·a_10_39·b_5_20 + a_2_3·b_2_5·a_10_39·b_5_19
       + a_2_3·b_2_57·b_2_6·a_1_0 + a_2_32·b_2_52·b_2_63·b_5_20
       + a_2_32·b_2_52·b_2_63·b_5_19 + a_2_32·b_2_54·b_2_6·b_5_20
       + a_2_32·b_2_55·b_5_20 + a_2_3·b_2_63·a_10_39·a_1_0
       + a_2_3·b_2_52·b_2_6·a_10_39·a_1_0 + a_2_3·b_2_53·a_10_39·a_1_0
       + a_2_32·a_10_39·b_5_20 + a_2_32·b_2_56·b_2_6·a_1_0
       + a_2_33·b_2_52·b_2_62·b_5_19 + a_2_33·b_2_53·b_2_6·b_5_19
       + a_2_3·c_16_113·b_1_2
  61. a_10_39·b_9_44 + a_10_39·b_9_41 + b_2_6·a_10_39·b_1_27 + b_2_62·a_1_0·b_5_19·b_9_41
       + b_2_63·b_1_24·a_9_29 + b_2_64·b_1_22·a_9_29 + b_2_64·a_10_39·b_1_2
       + b_2_52·a_10_39·b_5_19 + b_2_4·b_2_63·a_10_39·b_1_2
       + b_2_42·b_2_62·a_10_39·b_1_2 + b_2_43·b_2_6·a_10_39·b_1_2 + a_2_3·b_2_66·b_5_20
       + a_2_3·b_2_66·b_5_19 + a_2_3·b_2_52·b_2_64·b_5_20 + a_2_3·b_2_52·b_2_64·b_5_19
       + a_2_3·b_2_54·b_2_62·b_5_20 + a_10_39·a_9_29 + b_2_64·a_1_02·b_9_41
       + b_2_53·b_2_6·a_10_39·a_1_0 + b_2_54·a_10_39·a_1_0 + a_2_3·b_2_6·a_10_39·b_5_20
       + a_2_3·b_2_68·a_1_0 + a_2_3·b_2_5·a_10_39·b_5_19 + a_2_32·b_2_65·b_5_20
       + a_2_32·b_2_65·b_5_19 + a_2_32·b_2_5·b_2_64·b_5_19
       + a_2_32·b_2_52·b_2_63·b_5_20 + a_2_32·b_2_52·b_2_63·b_5_19
       + a_2_32·b_2_53·b_2_62·b_5_20 + a_2_32·b_2_54·b_2_6·b_5_19
       + a_2_32·b_2_55·b_5_20 + b_2_6·a_10_39·a_1_02·b_5_19 + b_2_68·a_1_03
       + a_2_3·b_2_63·a_10_39·a_1_0 + a_2_3·b_2_52·b_2_6·a_10_39·a_1_0
       + a_2_3·b_2_53·a_10_39·a_1_0 + a_2_32·b_2_56·b_2_6·a_1_0
       + a_2_33·b_2_53·b_2_6·b_5_19 + a_2_33·b_2_54·b_5_19 + a_2_3·c_16_113·a_1_0
  62. b_2_4·b_2_62·b_5_20·b_9_41 + b_2_4·b_2_64·b_1_2·b_9_41
       + b_2_42·b_2_6·b_5_20·b_9_41 + b_2_42·b_2_63·b_1_2·b_9_41 + b_2_43·b_5_20·b_9_41
       + b_2_44·b_2_6·b_1_2·b_9_41 + b_2_45·b_1_2·b_9_41 + a_10_39·b_1_2·b_9_41
       + a_10_39·b_10_53 + b_2_62·a_10_39·b_1_26 + b_2_65·a_10_39
       + b_2_53·b_2_62·a_10_39 + b_2_42·b_2_63·a_10_39 + b_2_44·b_2_6·a_10_39
       + b_2_45·a_10_39 + a_2_3·b_2_64·b_5_19·b_5_20 + a_2_3·b_2_5·b_2_63·b_5_19·b_5_20
       + a_2_3·b_2_5·b_2_68 + a_2_3·b_2_52·b_2_62·b_5_19·b_5_20 + a_2_3·b_2_52·b_2_67
       + a_2_3·b_2_53·b_2_66 + a_2_3·b_2_54·b_2_65 + a_2_3·b_2_44·b_1_2·b_9_41
       + b_2_62·a_1_02·b_5_19·b_9_41 + a_2_3·b_2_52·b_2_62·a_10_39
       + a_2_3·b_2_53·b_2_6·a_10_39 + a_2_32·b_2_63·b_5_19·b_5_20
       + a_2_32·b_2_5·b_2_62·b_5_19·b_5_20 + a_2_32·b_2_5·b_2_67
       + a_2_32·b_2_52·b_2_6·b_5_19·b_5_20 + a_2_32·b_2_54·b_2_64
       + b_2_66·a_1_03·b_5_19 + a_2_3·b_2_68·a_1_02 + a_2_32·b_2_52·b_2_6·a_10_39
       + a_2_32·b_2_53·a_10_39 + a_2_33·b_2_55·b_2_62
  63. b_10_53·b_1_210 + b_10_532 + b_2_6·b_10_53·b_1_28 + b_2_62·b_10_53·b_1_26
       + b_2_63·b_10_53·b_1_24 + b_2_64·b_1_212 + b_2_65·b_1_210 + b_2_68·b_1_24
       + b_2_610 + b_2_56·b_2_64 + b_2_43·b_2_67 + b_2_44·b_2_66 + b_2_45·b_2_65
       + b_2_47·b_2_63 + b_2_48·b_2_62 + b_10_53·b_1_2·a_9_29 + b_10_53·a_1_1·b_1_29
       + a_10_39·b_1_210 + b_2_6·b_10_53·a_1_1·b_1_27 + b_2_62·a_10_39·b_1_26
       + b_2_63·a_10_39·b_1_24 + b_2_65·b_1_2·a_9_29 + b_2_42·b_2_63·a_10_39
       + b_2_43·b_2_62·a_10_39 + b_2_45·a_10_39 + a_2_3·b_2_44·b_1_2·b_9_41
       + a_2_3·b_2_48·b_2_6 + a_2_3·b_2_49 + a_2_32·b_2_68 + a_2_32·b_2_52·b_2_66
       + a_2_32·b_2_54·b_2_64 + a_2_32·b_2_56·b_2_62 + a_2_32·b_2_63·a_10_39
       + a_2_33·b_2_55·b_2_62 + c_16_113·b_1_24 + b_2_42·c_16_113
       + c_16_113·a_1_1·b_1_23 + a_2_3·b_2_4·c_16_113
  64. a_10_392 + a_2_3·b_2_64·a_10_39 + a_2_3·b_2_66·a_1_0·b_5_19
       + a_2_3·b_2_52·b_2_62·a_10_39 + a_2_3·b_2_55·b_2_6·a_1_0·b_5_19
       + a_2_32·b_2_63·b_5_19·b_5_20 + a_2_32·b_2_68 + a_2_32·b_2_5·b_2_67
       + a_2_32·b_2_52·b_2_66 + a_2_32·b_2_53·b_2_65 + a_2_32·b_2_54·b_2_64
       + a_2_32·b_2_55·b_2_63 + a_2_32·b_2_56·b_2_62 + a_2_32·b_2_57·b_2_6
       + a_2_3·b_2_68·a_1_02 + a_2_32·b_2_63·a_10_39 + a_2_32·b_2_5·b_2_62·a_10_39
       + a_2_32·b_2_54·b_2_6·a_1_0·b_5_19 + a_2_32·b_2_55·a_1_0·b_5_19
       + a_2_33·b_2_54·b_2_63 + a_2_32·c_16_113


About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Data used for Benson′s test

  • Benson′s completion test succeeded in degree 20.
  • The completion test was perfect: It applied in the last degree in which a generator or relation was found.
  • The following is a filter regular homogeneous system of parameters:
    1. c_16_113, a Duflot regular element of degree 16
    2. b_1_24 + b_2_62 + b_2_5·b_2_6 + b_2_52 + b_2_4·b_2_6 + b_2_42, an element of degree 4
    3. b_1_2·b_5_20 + b_2_5·b_2_62 + b_2_52·b_2_6 + b_2_4·b_2_62 + b_2_4·b_2_5·b_2_6
         + b_2_43, an element of degree 6
  • The Raw Filter Degree Type of that HSOP is [-1, 7, 17, 23].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].
  • We found that there exists some filter regular HSOP formed by the first term of the above HSOP, together with 2 elements of degree 2.


About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 1

  1. a_1_00, an element of degree 1
  2. a_1_10, an element of degree 1
  3. b_1_20, an element of degree 1
  4. a_2_30, an element of degree 2
  5. b_2_40, an element of degree 2
  6. b_2_50, an element of degree 2
  7. b_2_60, an element of degree 2
  8. b_5_190, an element of degree 5
  9. b_5_200, an element of degree 5
  10. a_9_290, an element of degree 9
  11. b_9_410, an element of degree 9
  12. b_9_440, an element of degree 9
  13. a_10_390, an element of degree 10
  14. b_10_530, an element of degree 10
  15. c_16_113c_1_016, an element of degree 16

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_00, an element of degree 1
  2. a_1_10, an element of degree 1
  3. b_1_2c_1_1, an element of degree 1
  4. a_2_30, an element of degree 2
  5. b_2_40, an element of degree 2
  6. b_2_50, an element of degree 2
  7. b_2_6c_1_22 + c_1_1·c_1_2, an element of degree 2
  8. b_5_19c_1_1·c_1_24 + c_1_14·c_1_2, an element of degree 5
  9. b_5_20c_1_1·c_1_24 + c_1_13·c_1_22, an element of degree 5
  10. a_9_290, an element of degree 9
  11. b_9_41c_1_1·c_1_28 + c_1_13·c_1_26 + c_1_14·c_1_25 + c_1_15·c_1_24
       + c_1_16·c_1_23 + c_1_18·c_1_2 + c_1_02·c_1_13·c_1_24
       + c_1_02·c_1_15·c_1_22 + c_1_04·c_1_1·c_1_24 + c_1_04·c_1_13·c_1_22
       + c_1_04·c_1_15 + c_1_08·c_1_1, an element of degree 9
  12. b_9_44c_1_1·c_1_28 + c_1_13·c_1_26 + c_1_14·c_1_25 + c_1_15·c_1_24
       + c_1_16·c_1_23 + c_1_17·c_1_22 + c_1_02·c_1_13·c_1_24
       + c_1_02·c_1_15·c_1_22 + c_1_04·c_1_1·c_1_24 + c_1_04·c_1_13·c_1_22
       + c_1_04·c_1_15 + c_1_08·c_1_1, an element of degree 9
  13. a_10_390, an element of degree 10
  14. b_10_53c_1_210 + c_1_1·c_1_29 + c_1_12·c_1_28 + c_1_17·c_1_23 + c_1_18·c_1_22
       + c_1_19·c_1_2 + c_1_02·c_1_14·c_1_24 + c_1_02·c_1_16·c_1_22
       + c_1_04·c_1_12·c_1_24 + c_1_04·c_1_14·c_1_22 + c_1_04·c_1_16
       + c_1_08·c_1_12, an element of degree 10
  15. c_16_113c_1_216 + c_1_18·c_1_28 + c_1_114·c_1_22 + c_1_115·c_1_2
       + c_1_02·c_1_14·c_1_210 + c_1_02·c_1_15·c_1_29 + c_1_02·c_1_16·c_1_28
       + c_1_02·c_1_110·c_1_24 + c_1_02·c_1_111·c_1_23 + c_1_02·c_1_112·c_1_22
       + c_1_04·c_1_12·c_1_210 + c_1_04·c_1_13·c_1_29 + c_1_04·c_1_16·c_1_26
       + c_1_04·c_1_17·c_1_25 + c_1_04·c_1_110·c_1_22 + c_1_04·c_1_111·c_1_2
       + c_1_04·c_1_112 + c_1_08·c_1_28 + c_1_08·c_1_12·c_1_26
       + c_1_08·c_1_13·c_1_25 + c_1_08·c_1_14·c_1_24 + c_1_08·c_1_15·c_1_23
       + c_1_08·c_1_17·c_1_2 + c_1_016, an element of degree 16

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_00, an element of degree 1
  2. a_1_10, an element of degree 1
  3. b_1_20, an element of degree 1
  4. a_2_30, an element of degree 2
  5. b_2_40, an element of degree 2
  6. b_2_5c_1_22, an element of degree 2
  7. b_2_6c_1_12, an element of degree 2
  8. b_5_19c_1_1·c_1_24 + c_1_14·c_1_2, an element of degree 5
  9. b_5_20c_1_12·c_1_23 + c_1_14·c_1_2, an element of degree 5
  10. a_9_290, an element of degree 9
  11. b_9_41c_1_1·c_1_28 + c_1_13·c_1_26 + c_1_15·c_1_24 + c_1_16·c_1_23, an element of degree 9
  12. b_9_44c_1_13·c_1_26 + c_1_14·c_1_25 + c_1_15·c_1_24 + c_1_16·c_1_23, an element of degree 9
  13. a_10_390, an element of degree 10
  14. b_10_53c_1_14·c_1_26 + c_1_110, an element of degree 10
  15. c_16_113c_1_13·c_1_213 + c_1_15·c_1_211 + c_1_16·c_1_210 + c_1_19·c_1_27
       + c_1_110·c_1_26 + c_1_111·c_1_25 + c_1_112·c_1_24 + c_1_116
       + c_1_04·c_1_14·c_1_28 + c_1_04·c_1_18·c_1_24 + c_1_08·c_1_28
       + c_1_08·c_1_14·c_1_24 + c_1_08·c_1_18 + c_1_016, an element of degree 16

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_00, an element of degree 1
  2. a_1_10, an element of degree 1
  3. b_1_2c_1_2, an element of degree 1
  4. a_2_30, an element of degree 2
  5. b_2_4c_1_22, an element of degree 2
  6. b_2_5c_1_22, an element of degree 2
  7. b_2_6c_1_1·c_1_2 + c_1_12, an element of degree 2
  8. b_5_19c_1_1·c_1_24 + c_1_12·c_1_23, an element of degree 5
  9. b_5_20c_1_25 + c_1_12·c_1_23 + c_1_14·c_1_2, an element of degree 5
  10. a_9_290, an element of degree 9
  11. b_9_41c_1_29 + c_1_12·c_1_27 + c_1_13·c_1_26 + c_1_14·c_1_25 + c_1_15·c_1_24
       + c_1_16·c_1_23 + c_1_18·c_1_2 + c_1_02·c_1_12·c_1_25
       + c_1_02·c_1_14·c_1_23 + c_1_04·c_1_25 + c_1_04·c_1_12·c_1_23
       + c_1_04·c_1_14·c_1_2 + c_1_08·c_1_2, an element of degree 9
  12. b_9_44c_1_29 + c_1_1·c_1_28 + c_1_12·c_1_27 + c_1_02·c_1_12·c_1_25
       + c_1_02·c_1_14·c_1_23 + c_1_04·c_1_25 + c_1_04·c_1_12·c_1_23
       + c_1_04·c_1_14·c_1_2 + c_1_08·c_1_2, an element of degree 9
  13. a_10_390, an element of degree 10
  14. b_10_53c_1_210 + c_1_1·c_1_29 + c_1_12·c_1_28 + c_1_13·c_1_27 + c_1_14·c_1_26
       + c_1_19·c_1_2 + c_1_110, an element of degree 10
  15. c_16_113c_1_14·c_1_212 + c_1_15·c_1_211 + c_1_17·c_1_29 + c_1_110·c_1_26
       + c_1_111·c_1_25 + c_1_113·c_1_23 + c_1_114·c_1_22 + c_1_116
       + c_1_02·c_1_13·c_1_211 + c_1_02·c_1_14·c_1_210 + c_1_02·c_1_19·c_1_25
       + c_1_02·c_1_110·c_1_24 + c_1_04·c_1_1·c_1_211 + c_1_04·c_1_12·c_1_210
       + c_1_04·c_1_14·c_1_28 + c_1_04·c_1_15·c_1_27 + c_1_04·c_1_16·c_1_26
       + c_1_04·c_1_18·c_1_24 + c_1_04·c_1_19·c_1_23 + c_1_04·c_1_110·c_1_22
       + c_1_08·c_1_28 + c_1_08·c_1_1·c_1_27 + c_1_08·c_1_12·c_1_26
       + c_1_08·c_1_13·c_1_25 + c_1_08·c_1_15·c_1_23 + c_1_08·c_1_16·c_1_22
       + c_1_08·c_1_18 + c_1_016, an element of degree 16


About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128




Simon A. King David J. Green
Fakultät für Mathematik und Informatik Fakultät für Mathematik und Informatik
Friedrich-Schiller-Universität Jena Friedrich-Schiller-Universität Jena
Ernst-Abbe-Platz 2 Ernst-Abbe-Platz 2
D-07743 Jena D-07743 Jena
Germany Germany

E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46184
Fax: +49 (0)3641 9-46162
Office: Zi. 3524, Ernst-Abbe-Platz 2
E-mail: david dot green at uni hyphen jena dot de
Tel: +49 3641 9-46166
Fax: +49 3641 9-46162
Office: Zi 3512, Ernst-Abbe-Platz 2



Last change: 25.08.2009