Cohomology of group number 2287 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 5 minimal generators and exponent 4.
  • It is non-abelian.
  • It has p-Rank 3.
  • Its center has rank 2.
  • 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 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 1) · (t12  −  t11  −  2·t10  −  t9  +  2·t8  +  4·t7  +  2·t6  −  2·t5  +  t4  +  2·t3  +  3·t2  +  2·t  +  1)
    (t  −  1)3 · (t2  +  1)2 · (t4  +  1)2
  • The a-invariants are -∞,-∞,-4,-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 11:

  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. b_1_3, an element of degree 1
  5. b_1_4, an element of degree 1
  6. a_6_20, a nilpotent element of degree 6
  7. a_6_28, a nilpotent element of degree 6
  8. b_6_27, an element of degree 6
  9. b_6_29, an element of degree 6
  10. b_6_30, an element of degree 6
  11. b_6_31, an element of degree 6
  12. c_8_50, a Duflot regular element of degree 8
  13. c_8_51, a Duflot regular element of degree 8
  14. b_11_93, an element of degree 11
  15. b_11_94, an element of degree 11

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

Ring relations

There are 54 minimal relations of maximal degree 22:

  1. b_1_2·b_1_3 + a_1_1·b_1_3 + a_1_0·b_1_3 + a_1_0·b_1_2 + a_1_12
  2. b_1_42 + b_1_2·b_1_4 + b_1_2·b_1_3 + a_1_1·b_1_4 + a_1_1·b_1_3 + a_1_0·b_1_4 + a_1_0·b_1_2
       + a_1_0·a_1_1 + a_1_02
  3. a_1_12·b_1_3 + a_1_12·b_1_2 + a_1_0·a_1_1·b_1_3 + a_1_0·a_1_1·b_1_2 + a_1_02·b_1_3
       + a_1_02·b_1_2 + a_1_13
  4. a_1_0·b_1_32 + a_1_12·b_1_3 + a_1_0·a_1_1·b_1_3 + a_1_02·b_1_2 + a_1_02·a_1_1
       + a_1_03
  5. a_1_03·a_1_12 + a_1_04·a_1_1
  6. a_1_02·a_1_12·b_1_2 + a_1_03·a_1_1·b_1_2 + a_1_04·b_1_2 + a_1_0·a_1_14
       + a_1_02·a_1_13 + a_1_03·a_1_12
  7. a_6_28·b_1_3 + a_6_20·b_1_3 + a_6_20·a_1_0 + a_1_04·a_1_1·b_1_2·b_1_4
       + a_1_0·a_1_15·b_1_4
  8. b_6_27·b_1_3 + b_6_27·a_1_0 + a_1_0·a_1_1·b_1_24·b_1_4 + a_6_20·a_1_0
       + a_1_04·a_1_1·b_1_2·b_1_4 + a_1_0·a_1_15·b_1_4
  9. a_1_1·b_1_25·b_1_4 + a_1_0·b_1_25·b_1_4 + a_1_0·b_1_26 + b_6_29·a_1_0 + b_6_27·a_1_0
       + a_6_28·b_1_2 + a_6_20·b_1_3 + a_6_20·b_1_2 + a_6_28·a_1_1 + a_6_28·a_1_0 + a_6_20·a_1_1
       + a_6_20·a_1_0 + a_1_04·a_1_1·b_1_2·b_1_4 + a_1_05·a_1_1·b_1_4
  10. b_6_29·b_1_3 + a_6_28·b_1_2 + a_6_28·a_1_1 + a_1_04·a_1_1·b_1_2·b_1_4
       + a_1_0·a_1_15·b_1_4 + a_1_05·a_1_1·b_1_4
  11. b_1_27 + b_6_30·b_1_2 + b_6_27·b_1_2 + a_1_1·b_1_26 + a_1_0·b_1_26 + b_6_30·a_1_1
       + b_6_27·a_1_1 + a_6_28·b_1_2 + a_6_20·b_1_3 + a_6_20·b_1_2 + a_1_0·a_1_1·b_1_24·b_1_4
       + a_1_0·a_1_1·b_1_25 + a_6_28·a_1_1 + a_6_20·a_1_1 + a_6_20·a_1_0
       + a_1_04·a_1_1·b_1_2·b_1_4 + a_1_0·a_1_15·b_1_4 + a_1_05·a_1_1·b_1_4
  12. a_1_1·b_1_25·b_1_4 + a_1_0·b_1_25·b_1_4 + b_6_30·a_1_0 + a_6_20·b_1_2 + a_6_28·a_1_0
       + a_6_20·a_1_1 + a_6_20·a_1_0 + a_1_0·a_1_15·b_1_4 + a_1_05·a_1_1·b_1_4
  13. b_6_31·b_1_2 + a_1_1·b_1_25·b_1_4 + a_1_0·b_1_25·b_1_4 + a_1_0·b_1_26 + b_6_31·a_1_1
       + a_6_28·b_1_2 + a_1_0·a_1_1·b_1_24·b_1_4 + a_1_0·a_1_1·b_1_25 + a_6_28·a_1_1
       + a_6_28·a_1_0 + a_6_20·a_1_0 + a_1_04·a_1_1·b_1_3·b_1_4 + a_1_05·a_1_1·b_1_4
  14. b_6_31·a_1_0 + a_6_20·b_1_3 + a_1_04·a_1_1·b_1_3·b_1_4
  15. a_6_28·a_1_0·a_1_12 + a_6_28·a_1_02·a_1_1 + a_6_28·a_1_03
  16. b_6_29·b_1_26 + b_6_29·b_6_30 + b_6_27·b_6_29 + a_6_28·b_1_26 + a_6_28·b_6_29
       + a_6_20·b_6_29 + a_6_28·a_1_1·b_1_24·b_1_4 + a_6_28·a_1_1·b_1_25 + a_6_282
       + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4 + a_6_20·a_1_02·a_1_13·b_1_4
  17. b_6_27·b_1_26 + b_6_27·b_6_30 + b_6_272 + b_6_29·a_1_1·b_1_24·b_1_4
       + b_6_27·a_1_0·b_1_25 + a_6_28·b_1_25·b_1_4 + a_6_28·b_1_26 + a_6_20·b_6_29
       + a_6_20·b_6_27 + a_6_28·a_1_1·b_1_24·b_1_4 + a_6_20·a_1_1·b_1_24·b_1_4 + a_6_202
       + a_6_20·a_1_02·a_1_13·b_1_4
  18. b_6_29·b_6_31 + b_6_29·a_1_1·b_1_24·b_1_4 + a_6_28·b_1_25·b_1_4 + a_6_28·b_1_26
       + a_6_28·b_6_29 + a_6_20·b_1_26 + a_6_20·b_6_30 + a_6_20·b_6_27 + a_6_28·a_1_1·b_1_25
       + a_6_282 + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4 + a_6_20·a_1_04·a_1_1·b_1_4
  19. b_6_27·b_6_31 + b_6_29·a_1_1·b_1_24·b_1_4 + b_6_27·a_1_1·b_1_24·b_1_4
       + b_6_27·a_1_0·b_1_24·b_1_4 + b_6_27·a_1_0·b_1_25 + a_6_28·b_1_25·b_1_4
       + a_6_28·b_1_26 + a_6_20·b_1_26 + a_6_20·b_6_30 + a_6_20·b_6_29 + a_6_20·b_6_27
       + a_6_28·a_1_1·b_1_24·b_1_4 + a_6_282 + a_6_20·a_1_0·b_1_25 + a_6_20·a_6_28
       + a_6_202 + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4 + a_6_20·a_1_04·a_1_1·b_1_4
  20. b_6_29·a_1_1·b_1_24·b_1_4 + a_6_28·b_1_25·b_1_4 + a_6_28·b_6_31 + a_6_28·b_6_30
       + a_6_20·b_1_26 + a_6_20·b_6_30 + a_6_20·b_6_29 + a_6_20·b_6_27
       + a_6_28·a_1_1·b_1_24·b_1_4 + a_6_282 + a_6_20·a_1_0·b_1_25 + a_6_20·a_6_28
       + a_6_202 + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4 + a_6_20·a_1_02·a_1_13·b_1_4
  21. b_6_29·a_1_1·b_1_24·b_1_4 + a_6_28·b_1_25·b_1_4 + a_6_28·b_6_30 + a_6_20·b_1_26
       + a_6_20·b_6_31 + a_6_20·b_6_30 + a_6_20·b_6_29 + a_6_20·b_6_27
       + a_6_28·a_1_1·b_1_24·b_1_4 + a_6_282 + a_6_20·a_1_1·b_1_24·b_1_4 + a_6_20·a_6_28
       + a_6_20·a_1_02·a_1_13·b_1_4 + a_6_20·a_1_04·a_1_1·b_1_4
  22. b_6_30·b_1_25·b_1_4 + b_6_30·b_1_26 + b_6_272 + b_6_30·a_1_1·b_1_25
       + b_6_30·a_1_0·b_1_25 + b_6_29·a_1_1·b_1_24·b_1_4 + b_6_29·a_1_1·b_1_25
       + b_6_27·a_1_0·b_1_24·b_1_4 + a_6_28·b_1_25·b_1_4 + a_6_28·b_6_30
       + a_6_20·b_1_25·b_1_4 + a_6_20·b_6_29 + a_6_20·b_6_27 + a_6_28·a_1_1·b_1_24·b_1_4
       + a_6_282 + a_6_20·a_1_1·b_1_24·b_1_4 + a_6_20·a_6_28 + a_6_202
       + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4 + c_8_50·b_1_24 + c_8_50·a_1_0·b_1_23
       + c_8_50·a_1_0·a_1_1·b_1_22 + c_8_50·a_1_0·a_1_12·b_1_2 + c_8_50·a_1_03·b_1_2
       + c_8_50·a_1_0·a_1_13 + c_8_50·a_1_04
  23. b_6_30·b_1_25·b_1_4 + b_6_30·b_1_26 + b_6_272 + b_6_30·a_1_1·b_1_25
       + b_6_30·a_1_0·b_1_25 + b_6_29·a_1_1·b_1_25 + b_6_27·a_1_1·b_1_24·b_1_4
       + b_6_27·a_1_0·b_1_25 + a_6_28·b_1_26 + a_6_28·b_6_30 + a_6_28·b_6_27 + a_6_20·b_6_30
       + a_6_20·b_6_27 + b_6_27·a_1_0·a_1_1·b_1_24 + a_6_28·a_1_1·b_1_24·b_1_4
       + a_6_28·a_1_1·b_1_25 + a_6_20·a_1_1·b_1_25 + a_6_20·a_6_28
       + a_6_20·a_1_04·a_1_1·b_1_4 + c_8_50·b_1_24 + c_8_50·a_1_0·a_1_12·b_1_2
       + c_8_50·a_1_02·a_1_1·b_1_2 + c_8_50·a_1_03·b_1_3 + c_8_50·a_1_0·a_1_13
       + c_8_50·a_1_02·a_1_12 + c_8_50·a_1_03·a_1_1
  24. b_6_31·b_1_36 + b_6_312 + b_6_30·b_1_35·b_1_4 + b_6_30·b_1_25·b_1_4 + b_6_302
       + b_6_27·b_1_26 + b_6_31·a_1_1·b_1_34·b_1_4 + b_6_31·a_1_1·b_1_35
       + b_6_30·a_1_1·b_1_35 + b_6_30·a_1_1·b_1_25 + b_6_29·a_1_1·b_1_24·b_1_4
       + b_6_29·a_1_1·b_1_25 + b_6_27·a_1_0·b_1_24·b_1_4 + b_6_27·a_1_0·b_1_25
       + a_6_28·b_1_25·b_1_4 + a_6_28·b_1_26 + a_6_28·b_6_30 + a_6_20·b_1_25·b_1_4
       + a_6_20·b_1_26 + a_6_20·b_6_29 + a_6_20·b_6_27 + a_6_28·a_1_1·b_1_24·b_1_4
       + a_6_20·a_1_1·b_1_24·b_1_4 + a_6_20·a_1_0·b_1_25 + a_6_20·a_6_28 + c_8_50·b_1_34
       + c_8_50·b_1_24 + c_8_50·a_1_0·b_1_23 + c_8_50·a_1_0·a_1_1·b_1_22
       + c_8_50·a_1_0·a_1_12·b_1_2 + c_8_50·a_1_03·b_1_2 + c_8_50·a_1_14
       + c_8_50·a_1_0·a_1_13 + c_8_50·a_1_02·a_1_12
  25. b_6_30·b_1_26 + b_6_292 + b_6_30·a_1_1·b_1_25 + b_6_29·a_1_1·b_1_24·b_1_4
       + b_6_27·a_1_1·b_1_25 + b_6_27·a_1_0·b_1_24·b_1_4 + a_6_28·b_1_26 + a_6_28·b_6_29
       + a_6_20·b_6_27 + a_6_282 + a_6_20·a_1_1·b_1_24·b_1_4 + a_6_20·a_1_1·b_1_25
       + a_6_20·a_1_0·b_1_25 + a_6_20·a_6_28 + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4
       + a_6_20·a_1_04·a_1_1·b_1_4 + c_8_51·b_1_24 + c_8_50·b_1_24
       + c_8_51·a_1_0·b_1_23 + c_8_51·a_1_0·a_1_1·b_1_22 + c_8_51·a_1_02·a_1_1·b_1_2
       + c_8_50·a_1_03·b_1_2 + c_8_50·a_1_02·a_1_12 + c_8_50·a_1_03·a_1_1
  26. b_6_30·b_1_26 + b_6_292 + b_6_30·a_1_1·b_1_25 + b_6_30·a_1_0·b_1_25
       + b_6_27·a_1_1·b_1_24·b_1_4 + b_6_27·a_1_1·b_1_25 + b_6_27·a_1_0·b_1_25
       + a_6_28·b_1_25·b_1_4 + a_6_28·b_6_27 + a_6_20·b_1_25·b_1_4 + a_6_20·b_1_26
       + a_6_20·b_6_29 + a_6_28·a_1_1·b_1_25 + a_6_20·a_1_1·b_1_24·b_1_4
       + a_6_20·a_1_0·b_1_25 + a_6_20·a_6_28 + a_6_20·a_1_04·a_1_1·b_1_4 + c_8_51·b_1_24
       + c_8_50·b_1_24 + c_8_51·a_1_03·b_1_2 + c_8_50·a_1_0·a_1_12·b_1_2
       + c_8_50·a_1_02·a_1_1·b_1_2 + c_8_50·a_1_0·a_1_13 + c_8_50·a_1_02·a_1_12
       + c_8_50·a_1_03·a_1_1
  27. b_6_30·b_1_26 + b_6_292 + b_6_30·a_1_1·b_1_25 + b_6_30·a_1_0·b_1_25
       + b_6_27·a_1_1·b_1_25 + b_6_27·a_1_0·b_1_24·b_1_4 + a_6_28·b_1_25·b_1_4
       + a_6_28·b_1_26 + a_6_28·b_6_30 + a_6_20·b_6_29 + a_6_20·b_6_27
       + b_6_27·a_1_0·a_1_1·b_1_24 + a_6_28·a_1_1·b_1_24·b_1_4 + a_6_282
       + a_6_20·a_1_1·b_1_25 + a_6_20·a_6_28 + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4
       + a_6_20·a_1_02·a_1_13·b_1_4 + a_6_20·a_1_04·a_1_1·b_1_4 + c_8_51·b_1_24
       + c_8_50·b_1_24 + c_8_50·a_1_0·b_1_23 + c_8_50·a_1_0·a_1_1·b_1_22
       + c_8_50·a_1_0·a_1_12·b_1_2 + c_8_50·a_1_03·b_1_2 + c_8_51·a_1_14
       + c_8_50·a_1_0·a_1_13
  28. b_6_30·a_1_0·b_1_25 + b_6_27·a_1_1·b_1_24·b_1_4 + b_6_27·a_1_0·b_1_24·b_1_4
       + b_6_27·a_1_0·b_1_25 + a_6_28·b_1_26 + a_6_28·b_6_30 + a_6_28·b_6_29 + a_6_28·b_6_27
       + a_6_20·b_1_25·b_1_4 + a_6_20·b_1_26 + a_6_20·b_6_27 + a_6_28·a_1_1·b_1_24·b_1_4
       + a_6_28·a_1_1·b_1_25 + a_6_20·a_1_1·b_1_25 + a_6_20·a_6_28
       + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4 + a_6_20·a_1_02·a_1_13·b_1_4
       + a_6_20·a_1_04·a_1_1·b_1_4 + c_8_51·a_1_0·b_1_23 + c_8_51·a_1_0·a_1_1·b_1_22
       + c_8_51·a_1_0·a_1_12·b_1_2 + c_8_50·a_1_0·a_1_12·b_1_2
       + c_8_50·a_1_02·a_1_1·b_1_2 + c_8_51·a_1_0·a_1_13 + c_8_50·a_1_0·a_1_13
       + c_8_50·a_1_03·a_1_1
  29. b_6_30·b_1_25·b_1_4 + b_6_292 + b_6_272 + b_6_29·a_1_1·b_1_24·b_1_4
       + b_6_29·a_1_1·b_1_25 + b_6_27·a_1_1·b_1_25 + a_6_28·b_6_30 + a_6_28·b_6_27
       + a_6_20·b_1_25·b_1_4 + a_6_20·b_1_26 + a_6_20·b_6_30 + a_6_20·b_6_27
       + b_6_27·a_1_0·a_1_1·b_1_24 + a_6_28·a_1_1·b_1_24·b_1_4
       + a_6_20·a_1_1·b_1_24·b_1_4 + a_6_20·a_1_1·b_1_25 + a_6_20·a_6_28 + a_6_202
       + a_6_20·a_1_04·a_1_1·b_1_4 + c_8_51·b_1_24 + c_8_51·a_1_02·a_1_12
       + c_8_50·a_1_14 + c_8_50·a_1_02·a_1_12
  30. b_6_30·b_1_26 + b_6_292 + b_6_30·a_1_1·b_1_25 + b_6_30·a_1_0·b_1_25
       + b_6_27·a_1_1·b_1_25 + b_6_27·a_1_0·b_1_24·b_1_4 + a_6_28·b_1_25·b_1_4
       + a_6_28·b_6_27 + a_6_20·b_1_26 + a_6_20·b_6_30 + a_6_20·b_6_29
       + b_6_27·a_1_0·a_1_1·b_1_24 + a_6_28·a_1_1·b_1_24·b_1_4 + a_6_282
       + a_6_20·a_1_1·b_1_25 + a_6_20·a_6_28 + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4
       + a_6_20·a_1_02·a_1_13·b_1_4 + c_8_51·b_1_24 + c_8_50·b_1_24
       + c_8_50·a_1_0·b_1_23 + c_8_50·a_1_0·a_1_1·b_1_22 + c_8_50·a_1_0·a_1_12·b_1_2
       + c_8_51·a_1_03·a_1_1 + c_8_50·a_1_0·a_1_13 + c_8_50·a_1_02·a_1_12
  31. b_6_30·b_1_25·b_1_4 + b_6_30·b_1_26 + b_6_272 + b_6_30·a_1_1·b_1_25
       + b_6_30·a_1_0·b_1_25 + b_6_29·a_1_1·b_1_25 + b_6_27·a_1_1·b_1_24·b_1_4
       + b_6_27·a_1_0·b_1_25 + a_6_20·b_1_26 + b_6_27·a_1_0·a_1_1·b_1_24
       + a_6_28·a_1_1·b_1_25 + a_6_20·a_1_1·b_1_25 + a_6_20·a_1_0·b_1_25 + a_6_202
       + a_6_20·a_1_04·a_1_1·b_1_4 + c_8_50·b_1_24 + c_8_51·a_1_04
       + c_8_50·a_1_02·a_1_12
  32. b_6_29·a_1_1·b_1_24·b_1_4 + b_6_27·a_1_1·b_1_24·b_1_4 + b_6_27·a_1_0·b_1_24·b_1_4
       + b_6_27·a_1_0·b_1_25 + a_6_28·b_1_25·b_1_4 + a_6_28·b_1_26 + a_6_28·b_6_27
       + a_6_20·b_1_25·b_1_4 + a_6_20·b_1_26 + a_6_20·b_6_29 + a_6_20·b_6_27
       + b_6_27·a_1_0·a_1_1·b_1_24 + a_6_28·a_1_1·b_1_24·b_1_4 + a_6_28·a_1_1·b_1_25
       + a_6_282 + a_6_20·a_1_1·b_1_24·b_1_4 + a_6_20·a_1_1·b_1_25
       + a_6_20·a_1_0·b_1_25 + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4
       + a_6_20·a_1_04·a_1_1·b_1_4 + c_8_50·a_1_0·b_1_23 + c_8_50·a_1_0·a_1_1·b_1_22
       + c_8_51·a_1_03·b_1_3 + c_8_50·a_1_02·a_1_1·b_1_2 + c_8_50·a_1_03·b_1_2
       + c_8_50·a_1_14 + c_8_50·a_1_02·a_1_12
  33. b_6_30·b_1_35·b_1_4 + b_6_30·b_1_26 + b_6_302 + b_6_27·b_1_26 + b_6_272
       + b_6_31·a_1_1·b_1_34·b_1_4 + b_6_31·a_1_1·b_1_35 + b_6_30·a_1_0·b_1_25
       + b_6_29·a_1_1·b_1_24·b_1_4 + b_6_27·a_1_1·b_1_24·b_1_4
       + b_6_27·a_1_0·b_1_24·b_1_4 + a_6_28·b_1_25·b_1_4 + a_6_28·b_1_26 + a_6_28·b_6_30
       + a_6_20·b_1_25·b_1_4 + a_6_20·b_6_29 + a_6_20·b_6_27 + b_6_27·a_1_0·a_1_1·b_1_24
       + a_6_28·a_1_1·b_1_24·b_1_4 + a_6_28·a_1_1·b_1_25 + a_6_282
       + a_6_20·a_1_1·b_1_24·b_1_4 + a_6_20·a_1_1·b_1_25 + a_6_20·a_1_0·b_1_25
       + a_6_20·a_6_28 + a_6_202 + a_6_20·a_1_02·a_1_13·b_1_4 + a_6_20·a_1_04·a_1_1·b_1_4
       + c_8_51·b_1_34 + c_8_50·a_1_0·b_1_23 + c_8_50·a_1_0·a_1_1·b_1_22
       + c_8_50·a_1_0·a_1_12·b_1_2 + c_8_50·a_1_03·b_1_2 + c_8_50·a_1_14
       + c_8_50·a_1_0·a_1_13
  34. b_1_2·b_11_93 + b_6_30·b_1_25·b_1_4 + b_6_27·b_6_29 + a_1_1·b_11_93
       + b_6_30·a_1_0·b_1_25 + b_6_27·a_1_0·b_1_24·b_1_4 + b_6_27·a_1_0·b_1_25
       + a_6_28·b_1_25·b_1_4 + a_6_28·b_6_30 + a_6_28·b_6_29 + a_6_20·b_1_25·b_1_4
       + a_6_20·b_6_29 + a_6_28·a_1_1·b_1_24·b_1_4 + a_6_28·a_1_1·b_1_25 + a_6_282
       + a_6_20·a_1_1·b_1_24·b_1_4 + a_6_20·a_1_0·b_1_25 + a_6_20·a_6_28 + a_6_202
       + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4 + a_6_20·a_1_04·a_1_1·b_1_4 + c_8_51·b_1_24
       + c_8_50·b_1_24 + c_8_51·a_1_1·b_1_23 + c_8_51·a_1_0·b_1_22·b_1_4
       + c_8_51·a_1_0·b_1_23 + c_8_50·a_1_1·b_1_22·b_1_4 + c_8_50·a_1_1·b_1_23
       + c_8_50·a_1_0·b_1_22·b_1_4 + c_8_50·a_1_0·b_1_23 + c_8_51·a_1_12·b_1_2·b_1_4
       + c_8_51·a_1_0·a_1_1·b_1_3·b_1_4 + c_8_50·a_1_0·a_1_1·b_1_3·b_1_4
       + c_8_50·a_1_0·a_1_1·b_1_22 + c_8_50·a_1_02·b_1_3·b_1_4
       + c_8_51·a_1_0·a_1_12·b_1_2 + c_8_50·a_1_0·a_1_12·b_1_4
       + c_8_50·a_1_02·a_1_1·b_1_4 + c_8_50·a_1_02·a_1_1·b_1_3 + c_8_50·a_1_03·b_1_4
       + c_8_50·a_1_03·b_1_2 + c_8_50·a_1_14 + c_8_50·a_1_0·a_1_13
       + c_8_50·a_1_02·a_1_12
  35. b_6_30·b_1_25·b_1_4 + b_6_30·b_1_26 + b_6_272 + a_1_0·b_11_93
       + b_6_30·a_1_1·b_1_25 + b_6_30·a_1_0·b_1_25 + b_6_29·a_1_1·b_1_24·b_1_4
       + b_6_29·a_1_1·b_1_25 + b_6_27·a_1_0·b_1_24·b_1_4 + a_6_28·b_1_25·b_1_4
       + a_6_28·b_6_30 + a_6_28·b_6_29 + a_6_28·b_6_27 + a_6_20·b_1_26 + a_6_20·b_6_29
       + a_6_20·b_6_27 + b_6_27·a_1_0·a_1_1·b_1_24 + a_6_282 + a_6_20·a_1_1·b_1_25
       + a_6_20·a_1_0·b_1_25 + a_6_202 + a_6_20·a_1_04·a_1_1·b_1_4 + c_8_50·b_1_24
       + c_8_50·a_1_0·b_1_23 + c_8_51·a_1_0·a_1_1·b_1_3·b_1_4
       + c_8_51·a_1_0·a_1_1·b_1_22 + c_8_51·a_1_02·b_1_2·b_1_4
       + c_8_50·a_1_12·b_1_2·b_1_4 + c_8_50·a_1_0·a_1_1·b_1_3·b_1_4
       + c_8_50·a_1_02·b_1_3·b_1_4 + c_8_50·a_1_02·b_1_2·b_1_4
       + c_8_51·a_1_0·a_1_12·b_1_4 + c_8_50·a_1_13·b_1_4 + c_8_50·a_1_0·a_1_12·b_1_4
       + c_8_50·a_1_0·a_1_12·b_1_2 + c_8_50·a_1_02·a_1_1·b_1_4
       + c_8_50·a_1_02·a_1_1·b_1_3 + c_8_50·a_1_02·a_1_1·b_1_2 + c_8_50·a_1_03·b_1_4
       + c_8_50·a_1_0·a_1_13 + c_8_50·a_1_02·a_1_12 + c_8_50·a_1_03·a_1_1
  36. b_1_3·b_11_93 + b_6_31·b_1_35·b_1_4 + b_6_312 + b_6_30·b_1_36
       + b_6_30·b_1_25·b_1_4 + b_6_302 + b_6_27·b_1_26 + b_6_31·a_1_1·b_1_35
       + b_6_30·a_1_1·b_1_25 + b_6_30·a_1_0·b_1_25 + b_6_29·a_1_1·b_1_25
       + b_6_27·a_1_1·b_1_24·b_1_4 + a_6_28·b_1_26 + a_6_28·b_6_27 + a_6_20·b_1_25·b_1_4
       + a_6_20·b_6_30 + a_6_20·b_6_27 + b_6_27·a_1_0·a_1_1·b_1_24 + a_6_28·a_1_1·b_1_25
       + a_6_282 + a_6_20·a_1_0·b_1_25 + a_6_202 + a_6_20·a_1_04·a_1_1·b_1_4
       + c_8_50·b_1_33·b_1_4 + c_8_50·b_1_24 + c_8_51·a_1_1·b_1_32·b_1_4
       + c_8_51·a_1_0·b_1_23 + c_8_50·a_1_1·b_1_32·b_1_4 + c_8_50·a_1_0·b_1_23
       + c_8_51·a_1_12·b_1_2·b_1_4 + c_8_51·a_1_0·a_1_1·b_1_2·b_1_4
       + c_8_50·a_1_0·a_1_1·b_1_2·b_1_4 + c_8_50·a_1_02·b_1_3·b_1_4
       + c_8_50·a_1_02·b_1_2·b_1_4 + c_8_51·a_1_13·b_1_4 + c_8_51·a_1_0·a_1_12·b_1_4
       + c_8_51·a_1_0·a_1_12·b_1_2 + c_8_51·a_1_02·a_1_1·b_1_3 + c_8_50·a_1_13·b_1_4
       + c_8_50·a_1_13·b_1_2 + c_8_50·a_1_0·a_1_12·b_1_4 + c_8_50·a_1_02·a_1_1·b_1_3
       + c_8_50·a_1_02·a_1_1·b_1_2 + c_8_50·a_1_0·a_1_13
  37. b_1_2·b_11_94 + b_6_30·b_1_26 + b_6_29·b_1_25·b_1_4 + b_6_29·b_1_26
       + b_6_27·b_1_25·b_1_4 + b_6_27·b_1_26 + b_6_27·b_6_29 + a_1_1·b_11_94
       + b_6_29·a_1_1·b_1_25 + b_6_27·a_1_1·b_1_25 + a_6_28·b_1_25·b_1_4
       + a_6_28·b_1_26 + a_6_28·b_6_27 + a_6_20·b_6_30 + a_6_28·a_1_1·b_1_24·b_1_4
       + a_6_28·a_1_1·b_1_25 + a_6_20·a_1_1·b_1_25 + a_6_20·a_1_0·b_1_25 + a_6_20·a_6_28
       + a_6_202 + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4 + a_6_20·a_1_04·a_1_1·b_1_4
       + c_8_51·b_1_23·b_1_4 + c_8_51·a_1_0·b_1_23 + c_8_50·a_1_1·b_1_22·b_1_4
       + c_8_50·a_1_0·b_1_23 + c_8_51·a_1_12·b_1_2·b_1_4 + c_8_51·a_1_0·a_1_1·b_1_3·b_1_4
       + c_8_51·a_1_0·a_1_1·b_1_2·b_1_4 + c_8_51·a_1_02·b_1_3·b_1_4
       + c_8_50·a_1_0·a_1_1·b_1_2·b_1_4 + c_8_50·a_1_0·a_1_1·b_1_22
       + c_8_50·a_1_02·b_1_2·b_1_4 + c_8_51·a_1_13·b_1_4 + c_8_51·a_1_13·b_1_2
       + c_8_51·a_1_0·a_1_12·b_1_4 + c_8_51·a_1_02·a_1_1·b_1_4
       + c_8_51·a_1_02·a_1_1·b_1_3 + c_8_51·a_1_03·b_1_4 + c_8_50·a_1_13·b_1_4
       + c_8_50·a_1_13·b_1_2 + c_8_50·a_1_0·a_1_12·b_1_4 + c_8_50·a_1_0·a_1_12·b_1_2
       + c_8_50·a_1_02·a_1_1·b_1_4 + c_8_50·a_1_02·a_1_1·b_1_2 + c_8_50·a_1_03·b_1_4
       + c_8_50·a_1_14 + c_8_50·a_1_0·a_1_13 + c_8_50·a_1_02·a_1_12
       + c_8_50·a_1_03·a_1_1
  38. b_6_30·b_1_25·b_1_4 + b_6_30·b_1_26 + b_6_272 + a_1_0·b_11_94
       + b_6_30·a_1_1·b_1_25 + b_6_29·a_1_1·b_1_24·b_1_4 + b_6_29·a_1_1·b_1_25
       + b_6_27·a_1_0·b_1_25 + a_6_20·b_1_25·b_1_4 + a_6_20·b_1_26 + a_6_20·b_6_30
       + a_6_20·b_6_29 + a_6_28·a_1_1·b_1_25 + a_6_282 + a_6_20·a_1_1·b_1_24·b_1_4
       + a_6_20·a_1_1·b_1_25 + a_6_20·a_1_02·a_1_13·b_1_4 + c_8_50·b_1_24
       + c_8_51·a_1_0·b_1_22·b_1_4 + c_8_50·a_1_0·b_1_23 + c_8_51·a_1_12·b_1_2·b_1_4
       + c_8_51·a_1_0·a_1_1·b_1_3·b_1_4 + c_8_51·a_1_02·b_1_3·b_1_4
       + c_8_50·a_1_12·b_1_2·b_1_4 + c_8_50·a_1_0·a_1_1·b_1_22 + c_8_51·a_1_13·b_1_4
       + c_8_51·a_1_0·a_1_12·b_1_2 + c_8_51·a_1_02·a_1_1·b_1_4
       + c_8_51·a_1_02·a_1_1·b_1_3 + c_8_51·a_1_03·b_1_4 + c_8_50·a_1_13·b_1_4
       + c_8_50·a_1_13·b_1_2 + c_8_50·a_1_0·a_1_12·b_1_4 + c_8_50·a_1_0·a_1_12·b_1_2
       + c_8_50·a_1_02·a_1_1·b_1_2 + c_8_50·a_1_03·b_1_4 + c_8_50·a_1_14
       + c_8_50·a_1_0·a_1_13
  39. b_1_3·b_11_94 + b_6_31·b_1_36 + b_6_30·b_1_36 + b_6_30·b_1_25·b_1_4
       + b_6_30·b_1_26 + b_6_30·b_6_31 + b_6_272 + b_6_31·a_1_1·b_1_34·b_1_4
       + b_6_30·a_1_1·b_1_34·b_1_4 + b_6_30·a_1_1·b_1_25 + b_6_30·a_1_0·b_1_25
       + b_6_29·a_1_1·b_1_25 + b_6_27·a_1_1·b_1_24·b_1_4 + b_6_27·a_1_0·b_1_24·b_1_4
       + b_6_27·a_1_0·b_1_25 + a_6_28·b_1_25·b_1_4 + a_6_28·b_1_26 + a_6_28·b_6_30
       + a_6_28·b_6_29 + a_6_28·b_6_27 + a_6_20·b_1_25·b_1_4 + a_6_20·b_6_30
       + b_6_27·a_1_0·a_1_1·b_1_24 + a_6_28·a_1_1·b_1_25 + a_6_20·a_1_1·b_1_24·b_1_4
       + a_6_20·a_6_28 + a_6_20·a_1_03·a_1_1·b_1_2·b_1_4 + a_6_20·a_1_02·a_1_13·b_1_4
       + c_8_51·b_1_33·b_1_4 + c_8_50·b_1_33·b_1_4 + c_8_50·b_1_24
       + c_8_51·a_1_1·b_1_32·b_1_4 + c_8_51·a_1_0·b_1_22·b_1_4 + c_8_51·a_1_0·b_1_23
       + c_8_50·a_1_1·b_1_33 + c_8_51·a_1_12·b_1_2·b_1_4 + c_8_51·a_1_0·a_1_1·b_1_3·b_1_4
       + c_8_51·a_1_0·a_1_1·b_1_22 + c_8_51·a_1_02·b_1_3·b_1_4
       + c_8_51·a_1_02·b_1_2·b_1_4 + c_8_50·a_1_12·b_1_2·b_1_4
       + c_8_50·a_1_02·b_1_3·b_1_4 + c_8_51·a_1_0·a_1_12·b_1_4
       + c_8_51·a_1_0·a_1_12·b_1_2 + c_8_50·a_1_0·a_1_12·b_1_2
       + c_8_50·a_1_02·a_1_1·b_1_4 + c_8_50·a_1_02·a_1_1·b_1_3 + c_8_50·a_1_03·b_1_4
       + c_8_50·a_1_03·b_1_2 + c_8_50·a_1_0·a_1_13 + c_8_50·a_1_02·a_1_12
  40. b_6_29·b_11_93 + b_6_29·b_6_30·b_1_24·b_1_4 + b_6_27·b_6_30·b_1_25
       + b_6_272·a_1_1·b_1_24 + a_6_20·b_6_30·b_1_25 + a_6_20·b_6_27·b_1_24·b_1_4
       + a_6_20·b_6_27·b_1_25 + a_6_20·b_6_30·a_1_1·b_1_24
       + a_6_20·b_6_29·a_1_1·b_1_24 + a_6_20·b_6_27·a_1_0·b_1_24 + a_6_202·b_1_25
       + b_6_29·c_8_51·b_1_23 + b_6_29·c_8_50·b_1_23 + b_6_27·c_8_51·b_1_23
       + b_6_27·c_8_50·b_1_23 + b_6_30·c_8_50·a_1_0·b_1_22
       + b_6_29·c_8_50·a_1_1·b_1_2·b_1_4 + b_6_27·c_8_51·a_1_1·b_1_22
       + b_6_27·c_8_51·a_1_0·b_1_2·b_1_4 + b_6_27·c_8_50·a_1_1·b_1_22
       + b_6_27·c_8_50·a_1_0·b_1_22 + a_6_28·c_8_51·b_1_22·b_1_4
       + a_6_28·c_8_50·b_1_22·b_1_4 + a_6_20·c_8_51·b_1_22·b_1_4
       + b_6_27·c_8_51·a_1_0·a_1_1·b_1_4 + a_6_28·c_8_51·a_1_1·b_1_2·b_1_4
       + a_6_28·c_8_51·a_1_1·b_1_22 + a_6_28·c_8_50·a_1_1·b_1_2·b_1_4
       + a_6_20·c_8_51·a_1_1·b_1_22 + a_6_20·c_8_51·a_1_0·b_1_2·b_1_4
       + a_6_20·c_8_50·a_1_1·b_1_22 + a_6_20·c_8_50·a_1_0·b_1_2·b_1_4
       + b_6_27·c_8_50·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_02·b_1_4
       + a_6_28·c_8_50·a_1_02·b_1_4 + a_6_20·c_8_51·a_1_12·b_1_2
       + a_6_20·c_8_51·a_1_02·b_1_2 + a_6_20·c_8_50·a_1_0·a_1_1·b_1_4
       + a_6_20·c_8_50·a_1_02·b_1_4 + a_6_20·c_8_50·a_1_02·b_1_2 + a_6_28·c_8_51·a_1_13
       + a_6_28·c_8_51·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_03 + a_6_20·c_8_51·a_1_0·a_1_12
       + a_6_20·c_8_51·a_1_02·a_1_1 + a_6_20·c_8_51·a_1_03 + a_6_20·c_8_50·a_1_0·a_1_12
       + a_6_20·c_8_50·a_1_03
  41. b_6_29·b_6_30·b_1_24·b_1_4 + b_6_29·b_6_30·b_1_25 + b_6_27·b_11_93
       + b_6_27·b_6_30·b_1_24·b_1_4 + b_6_27·b_6_30·a_1_0·b_1_24
       + b_6_27·b_6_29·a_1_1·b_1_23·b_1_4 + b_6_272·a_1_1·b_1_24
       + a_6_28·b_6_30·b_1_25 + a_6_28·b_6_27·b_1_24·b_1_4 + a_6_28·b_6_27·b_1_25
       + a_6_20·b_6_30·b_1_25 + a_6_20·b_6_29·b_1_24·b_1_4 + a_6_20·b_6_29·b_1_25
       + a_6_28·b_6_27·a_1_1·b_1_24 + a_6_20·b_6_30·a_1_1·b_1_24
       + a_6_20·b_6_29·a_1_1·b_1_24 + a_6_20·b_6_27·a_1_1·b_1_24
       + a_6_20·a_6_28·b_1_25 + a_6_202·b_1_25 + b_6_29·c_8_50·b_1_23
       + b_6_27·c_8_51·b_1_23 + b_6_27·c_8_50·b_1_23 + b_6_30·c_8_51·a_1_1·b_1_22
       + b_6_30·c_8_50·a_1_0·b_1_22 + b_6_29·c_8_50·a_1_1·b_1_22
       + b_6_27·c_8_51·a_1_1·b_1_22 + b_6_27·c_8_51·a_1_0·b_1_2·b_1_4
       + b_6_27·c_8_50·a_1_1·b_1_2·b_1_4 + b_6_27·c_8_50·a_1_0·b_1_22
       + a_6_20·c_8_50·b_1_22·b_1_4 + b_6_27·c_8_51·a_1_02·b_1_4
       + b_6_27·c_8_50·a_1_0·a_1_1·b_1_4 + b_6_27·c_8_50·a_1_0·a_1_1·b_1_2
       + a_6_28·c_8_51·a_1_1·b_1_22 + a_6_28·c_8_50·a_1_1·b_1_22
       + a_6_20·c_8_51·a_1_0·b_1_2·b_1_4 + a_6_20·c_8_50·a_1_1·b_1_22
       + a_6_20·c_8_50·a_1_0·b_1_2·b_1_4 + b_6_27·c_8_51·a_1_02·a_1_1
       + b_6_27·c_8_50·a_1_02·a_1_1 + a_6_20·c_8_51·a_1_02·b_1_4
       + a_6_20·c_8_51·a_1_02·b_1_2 + a_6_20·c_8_50·a_1_12·b_1_4
       + a_6_20·c_8_50·a_1_02·b_1_4 + a_6_20·c_8_50·a_1_02·b_1_2
       + a_6_28·c_8_51·a_1_02·a_1_1 + a_6_28·c_8_50·a_1_13 + a_6_20·c_8_51·a_1_0·a_1_12
       + a_6_20·c_8_51·a_1_02·a_1_1 + a_6_20·c_8_50·a_1_13
  42. b_6_27·b_6_30·a_1_0·b_1_24 + a_6_28·b_11_93 + a_6_28·b_6_30·b_1_25
       + a_6_20·b_6_29·b_1_24·b_1_4 + a_6_20·b_6_29·b_1_25 + a_6_20·b_6_30·a_1_1·b_1_24
       + a_6_20·a_6_28·b_1_25 + b_6_27·c_8_51·a_1_0·b_1_22
       + b_6_27·c_8_50·a_1_0·b_1_22 + a_6_28·c_8_51·b_1_23 + a_6_28·c_8_50·b_1_23
       + b_6_27·c_8_50·a_1_0·a_1_1·b_1_2 + b_6_27·c_8_50·a_1_02·b_1_4
       + a_6_28·c_8_50·a_1_1·b_1_2·b_1_4 + a_6_20·c_8_51·a_1_1·b_1_3·b_1_4
       + a_6_20·c_8_51·a_1_0·b_1_22 + a_6_20·c_8_50·a_1_1·b_1_3·b_1_4
       + a_6_20·c_8_50·a_1_1·b_1_22 + b_6_27·c_8_51·a_1_02·a_1_1
       + a_6_28·c_8_50·a_1_02·b_1_4 + a_6_20·c_8_51·a_1_12·b_1_4
       + a_6_20·c_8_51·a_1_12·b_1_2 + a_6_20·c_8_51·a_1_0·a_1_1·b_1_2
       + a_6_20·c_8_51·a_1_02·b_1_4 + a_6_20·c_8_50·a_1_12·b_1_2
       + a_6_20·c_8_50·a_1_0·a_1_1·b_1_4 + a_6_20·c_8_50·a_1_0·a_1_1·b_1_2
       + a_6_28·c_8_51·a_1_13 + a_6_28·c_8_51·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_03
       + a_6_20·c_8_51·a_1_0·a_1_12 + a_6_20·c_8_51·a_1_02·a_1_1 + a_6_20·c_8_51·a_1_03
       + a_6_20·c_8_50·a_1_0·a_1_12 + a_6_20·c_8_50·a_1_03
  43. b_6_31·b_11_93 + b_6_312·b_1_34·b_1_4 + b_6_312·b_1_35
       + b_6_30·b_6_31·b_1_34·b_1_4 + b_6_30·b_6_31·b_1_35 + b_6_312·a_1_1·b_1_33·b_1_4
       + b_6_30·b_6_31·a_1_1·b_1_34 + b_6_27·b_6_29·a_1_1·b_1_23·b_1_4
       + a_6_28·b_6_30·b_1_25 + a_6_28·b_6_27·b_1_24·b_1_4 + a_6_28·b_6_27·b_1_25
       + a_6_20·b_6_30·b_1_24·b_1_4 + a_6_20·b_6_29·b_1_24·b_1_4 + a_6_20·b_6_29·b_1_25
       + a_6_20·b_6_27·b_1_24·b_1_4 + a_6_20·b_6_27·b_1_25 + a_6_20·b_6_30·a_1_1·b_1_24
       + a_6_20·b_6_29·a_1_1·b_1_23·b_1_4 + a_6_20·b_6_27·a_1_1·b_1_24
       + a_6_20·a_6_28·b_1_25 + a_6_202·b_1_25 + b_6_31·c_8_50·b_1_32·b_1_4
       + b_6_31·c_8_50·b_1_33 + b_6_31·c_8_51·a_1_1·b_1_3·b_1_4
       + b_6_31·c_8_50·a_1_1·b_1_3·b_1_4 + a_6_28·c_8_51·b_1_23 + a_6_28·c_8_50·b_1_23
       + a_6_20·c_8_51·b_1_23 + a_6_20·c_8_50·b_1_23 + b_6_27·c_8_51·a_1_02·b_1_4
       + b_6_27·c_8_50·a_1_0·a_1_1·b_1_2 + a_6_28·c_8_50·a_1_1·b_1_2·b_1_4
       + a_6_20·c_8_51·a_1_1·b_1_22 + a_6_20·c_8_50·a_1_1·b_1_3·b_1_4
       + b_6_27·c_8_51·a_1_02·a_1_1 + b_6_27·c_8_50·a_1_02·a_1_1
       + a_6_28·c_8_51·a_1_02·b_1_4 + a_6_28·c_8_50·a_1_02·b_1_4
       + a_6_20·c_8_51·a_1_0·a_1_1·b_1_2 + a_6_20·c_8_51·a_1_02·b_1_2
       + a_6_20·c_8_50·a_1_12·b_1_4 + a_6_20·c_8_50·a_1_0·a_1_1·b_1_2
       + a_6_28·c_8_51·a_1_13 + a_6_28·c_8_51·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_03
       + a_6_28·c_8_50·a_1_03 + a_6_20·c_8_51·a_1_13 + a_6_20·c_8_51·a_1_0·a_1_12
       + a_6_20·c_8_50·a_1_03
  44. b_6_30·b_11_93 + b_6_30·b_6_31·b_1_34·b_1_4 + b_6_30·b_6_31·b_1_35
       + b_6_302·b_1_35 + b_6_29·b_6_30·b_1_24·b_1_4 + b_6_29·b_6_30·b_1_25
       + b_6_292·b_1_25 + b_6_27·b_6_30·b_1_24·b_1_4 + b_6_27·b_6_29·b_1_25
       + b_6_272·b_1_25 + b_6_312·a_1_1·b_1_33·b_1_4
       + b_6_30·b_6_31·a_1_1·b_1_33·b_1_4 + b_6_302·a_1_1·b_1_34
       + b_6_29·b_6_30·a_1_1·b_1_24 + b_6_27·b_6_30·a_1_1·b_1_24
       + b_6_27·b_6_30·a_1_0·b_1_24 + a_6_28·b_6_30·b_1_25 + a_6_28·b_6_29·b_1_25
       + a_6_20·b_6_30·b_1_25 + a_6_20·b_6_29·b_1_24·b_1_4 + a_6_20·b_6_29·b_1_25
       + a_6_28·b_6_27·a_1_1·b_1_24 + a_6_20·b_6_30·a_1_1·b_1_24
       + a_6_20·b_6_29·a_1_1·b_1_23·b_1_4 + a_6_20·b_6_29·a_1_1·b_1_24
       + a_6_20·b_6_27·a_1_0·b_1_24 + a_6_20·a_6_28·b_1_25 + c_8_51·b_1_38·b_1_4
       + b_6_30·c_8_50·b_1_32·b_1_4 + b_6_30·c_8_50·b_1_33 + b_6_30·c_8_50·b_1_23
       + b_6_29·c_8_50·b_1_23 + b_6_27·c_8_51·b_1_23 + c_8_51·a_1_1·b_1_37·b_1_4
       + c_8_50·a_1_1·b_1_37·b_1_4 + b_6_30·c_8_51·a_1_1·b_1_3·b_1_4
       + b_6_30·c_8_51·a_1_1·b_1_22 + b_6_30·c_8_51·a_1_0·b_1_22
       + b_6_30·c_8_50·a_1_1·b_1_3·b_1_4 + b_6_30·c_8_50·a_1_0·b_1_22
       + b_6_29·c_8_50·a_1_1·b_1_22 + b_6_27·c_8_51·a_1_1·b_1_22
       + b_6_27·c_8_51·a_1_0·b_1_22 + b_6_27·c_8_50·a_1_1·b_1_2·b_1_4
       + b_6_27·c_8_50·a_1_0·b_1_2·b_1_4 + a_6_28·c_8_51·b_1_23 + a_6_28·c_8_50·b_1_23
       + a_6_20·c_8_51·b_1_22·b_1_4 + b_6_27·c_8_51·a_1_02·b_1_4
       + b_6_27·c_8_50·a_1_02·b_1_4 + a_6_28·c_8_51·a_1_1·b_1_22
       + a_6_28·c_8_50·a_1_1·b_1_2·b_1_4 + a_6_20·c_8_51·a_1_1·b_1_22
       + a_6_20·c_8_51·a_1_0·b_1_2·b_1_4 + a_6_20·c_8_51·a_1_0·b_1_22
       + a_6_20·c_8_50·a_1_1·b_1_3·b_1_4 + a_6_20·c_8_50·a_1_0·b_1_2·b_1_4
       + b_6_27·c_8_51·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_02·b_1_4
       + a_6_28·c_8_50·a_1_12·b_1_4 + a_6_28·c_8_50·a_1_0·a_1_1·b_1_4
       + a_6_28·c_8_50·a_1_02·b_1_4 + a_6_20·c_8_51·a_1_12·b_1_4
       + a_6_20·c_8_51·a_1_0·a_1_1·b_1_4 + a_6_20·c_8_51·a_1_02·b_1_4
       + a_6_20·c_8_51·a_1_02·b_1_2 + a_6_20·c_8_50·a_1_12·b_1_4
       + a_6_20·c_8_50·a_1_12·b_1_2 + a_6_20·c_8_50·a_1_02·b_1_4
       + a_6_20·c_8_50·a_1_02·b_1_2 + a_6_28·c_8_50·a_1_02·a_1_1 + a_6_28·c_8_50·a_1_03
       + a_6_20·c_8_51·a_1_03 + a_6_20·c_8_50·a_1_13
  45. b_6_27·b_6_29·a_1_1·b_1_23·b_1_4 + a_6_28·b_6_27·b_1_24·b_1_4
       + a_6_28·b_6_27·b_1_25 + a_6_20·b_11_93 + a_6_20·b_6_30·b_1_24·b_1_4
       + a_6_20·b_6_29·b_1_24·b_1_4 + a_6_20·b_6_29·b_1_25 + a_6_28·b_6_27·a_1_1·b_1_24
       + a_6_20·b_6_30·a_1_1·b_1_24 + a_6_20·b_6_27·a_1_1·b_1_24
       + a_6_28·c_8_50·b_1_23 + a_6_20·c_8_51·b_1_23 + a_6_20·c_8_50·b_1_23
       + b_6_27·c_8_51·a_1_0·a_1_1·b_1_2 + b_6_27·c_8_50·a_1_0·a_1_1·b_1_2
       + b_6_27·c_8_50·a_1_02·b_1_4 + a_6_28·c_8_50·a_1_1·b_1_22
       + a_6_20·c_8_51·a_1_1·b_1_3·b_1_4 + a_6_20·c_8_51·a_1_1·b_1_22
       + a_6_20·c_8_51·a_1_0·b_1_2·b_1_4 + a_6_20·c_8_50·a_1_1·b_1_3·b_1_4
       + a_6_20·c_8_50·a_1_1·b_1_2·b_1_4 + a_6_20·c_8_50·a_1_1·b_1_22
       + b_6_27·c_8_51·a_1_02·a_1_1 + b_6_27·c_8_50·a_1_02·a_1_1
       + a_6_28·c_8_50·a_1_12·b_1_4 + a_6_28·c_8_50·a_1_0·a_1_1·b_1_4
       + a_6_20·c_8_51·a_1_12·b_1_4 + a_6_20·c_8_50·a_1_12·b_1_2
       + a_6_20·c_8_50·a_1_0·a_1_1·b_1_2 + a_6_20·c_8_50·a_1_02·b_1_4
       + a_6_28·c_8_51·a_1_13 + a_6_28·c_8_51·a_1_03 + a_6_28·c_8_50·a_1_13
       + a_6_28·c_8_50·a_1_02·a_1_1 + a_6_20·c_8_51·a_1_13 + a_6_20·c_8_51·a_1_02·a_1_1
       + a_6_20·c_8_50·a_1_13 + a_6_20·c_8_50·a_1_03
  46. b_6_29·b_11_94 + b_6_29·b_6_30·b_1_25 + b_6_27·b_6_30·b_1_25
       + b_6_27·b_6_29·b_1_24·b_1_4 + b_6_27·b_6_29·b_1_25 + b_6_272·b_1_25
       + b_6_27·b_6_30·a_1_1·b_1_24 + b_6_27·b_6_30·a_1_0·b_1_24
       + b_6_27·b_6_29·a_1_1·b_1_23·b_1_4 + b_6_27·b_6_29·a_1_1·b_1_24
       + a_6_28·b_6_29·b_1_25 + a_6_28·b_6_27·b_1_25 + a_6_20·b_6_30·b_1_25
       + a_6_20·b_6_29·b_1_25 + a_6_20·b_6_27·b_1_25 + a_6_20·b_6_27·a_1_1·b_1_24
       + a_6_20·a_6_28·b_1_25 + a_6_202·b_1_25 + b_6_30·c_8_51·b_1_22·b_1_4
       + b_6_30·c_8_51·b_1_23 + b_6_30·c_8_50·b_1_22·b_1_4 + b_6_29·c_8_51·b_1_22·b_1_4
       + b_6_27·c_8_51·b_1_22·b_1_4 + b_6_27·c_8_50·b_1_22·b_1_4 + b_6_27·c_8_50·b_1_23
       + b_6_30·c_8_51·a_1_0·b_1_22 + b_6_29·c_8_51·a_1_1·b_1_2·b_1_4
       + b_6_29·c_8_50·a_1_1·b_1_2·b_1_4 + b_6_27·c_8_51·a_1_1·b_1_22
       + b_6_27·c_8_51·a_1_0·b_1_2·b_1_4 + b_6_27·c_8_50·a_1_1·b_1_22
       + b_6_27·c_8_50·a_1_0·b_1_2·b_1_4 + a_6_28·c_8_51·b_1_22·b_1_4
       + a_6_28·c_8_50·b_1_22·b_1_4 + a_6_20·c_8_51·b_1_23 + a_6_20·c_8_50·b_1_23
       + b_6_27·c_8_51·a_1_0·a_1_1·b_1_2 + a_6_28·c_8_51·a_1_1·b_1_2·b_1_4
       + a_6_20·c_8_51·a_1_1·b_1_2·b_1_4 + a_6_20·c_8_50·a_1_1·b_1_2·b_1_4
       + a_6_20·c_8_50·a_1_0·b_1_22 + b_6_27·c_8_51·a_1_02·a_1_1
       + b_6_27·c_8_50·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_0·a_1_1·b_1_4
       + a_6_20·c_8_51·a_1_12·b_1_2 + a_6_20·c_8_50·a_1_0·a_1_1·b_1_2
       + a_6_28·c_8_51·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_03 + a_6_28·c_8_50·a_1_13
       + a_6_28·c_8_50·a_1_02·a_1_1 + a_6_20·c_8_51·a_1_0·a_1_12 + a_6_20·c_8_51·a_1_03
       + a_6_20·c_8_50·a_1_13 + a_6_20·c_8_50·a_1_0·a_1_12 + a_6_20·c_8_50·a_1_03
  47. b_6_29·b_6_30·b_1_24·b_1_4 + b_6_29·b_6_30·b_1_25 + b_6_27·b_11_94
       + b_6_27·b_6_30·b_1_25 + b_6_27·b_6_29·b_1_24·b_1_4 + b_6_27·b_6_29·b_1_25
       + b_6_272·b_1_25 + b_6_27·b_6_30·a_1_1·b_1_24
       + b_6_27·b_6_29·a_1_1·b_1_23·b_1_4 + b_6_272·a_1_1·b_1_24
       + a_6_28·b_6_30·b_1_25 + a_6_28·b_6_27·b_1_24·b_1_4 + a_6_20·b_6_30·b_1_24·b_1_4
       + a_6_20·b_6_30·b_1_25 + a_6_20·b_6_29·b_1_24·b_1_4 + a_6_20·b_6_27·b_1_25
       + a_6_28·b_6_27·a_1_1·b_1_24 + a_6_20·b_6_29·a_1_1·b_1_24
       + a_6_20·b_6_27·a_1_0·b_1_24 + b_6_30·c_8_50·b_1_22·b_1_4 + b_6_29·c_8_50·b_1_23
       + b_6_27·c_8_51·b_1_22·b_1_4 + b_6_27·c_8_50·b_1_22·b_1_4
       + b_6_30·c_8_51·a_1_1·b_1_22 + b_6_30·c_8_50·a_1_0·b_1_22
       + b_6_29·c_8_50·a_1_1·b_1_22 + b_6_27·c_8_51·a_1_1·b_1_2·b_1_4
       + b_6_27·c_8_51·a_1_1·b_1_22 + b_6_27·c_8_51·a_1_0·b_1_22
       + b_6_27·c_8_50·a_1_1·b_1_2·b_1_4 + b_6_27·c_8_50·a_1_0·b_1_22
       + a_6_28·c_8_50·b_1_22·b_1_4 + a_6_28·c_8_50·b_1_23 + a_6_20·c_8_50·b_1_22·b_1_4
       + b_6_27·c_8_51·a_1_0·a_1_1·b_1_4 + b_6_27·c_8_51·a_1_0·a_1_1·b_1_2
       + b_6_27·c_8_51·a_1_02·b_1_4 + b_6_27·c_8_50·a_1_0·a_1_1·b_1_4
       + b_6_27·c_8_50·a_1_02·b_1_4 + a_6_28·c_8_51·a_1_1·b_1_22
       + a_6_20·c_8_51·a_1_1·b_1_22 + a_6_20·c_8_51·a_1_0·b_1_2·b_1_4
       + a_6_20·c_8_50·a_1_1·b_1_2·b_1_4 + a_6_20·c_8_50·a_1_0·b_1_22
       + b_6_27·c_8_50·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_12·b_1_4
       + a_6_28·c_8_51·a_1_0·a_1_1·b_1_4 + a_6_28·c_8_51·a_1_02·b_1_4
       + a_6_28·c_8_50·a_1_02·b_1_4 + a_6_20·c_8_51·a_1_12·b_1_2
       + a_6_20·c_8_51·a_1_0·a_1_1·b_1_2 + a_6_20·c_8_51·a_1_02·b_1_4
       + a_6_20·c_8_51·a_1_02·b_1_2 + a_6_20·c_8_50·a_1_0·a_1_1·b_1_4
       + a_6_20·c_8_50·a_1_0·a_1_1·b_1_2 + a_6_20·c_8_50·a_1_02·b_1_2
       + a_6_28·c_8_51·a_1_13 + a_6_28·c_8_51·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_03
       + a_6_28·c_8_50·a_1_02·a_1_1 + a_6_28·c_8_50·a_1_03 + a_6_20·c_8_50·a_1_13
       + a_6_20·c_8_50·a_1_02·a_1_1 + a_6_20·c_8_50·a_1_03
  48. b_6_27·b_6_30·a_1_0·b_1_24 + a_6_28·b_11_94 + a_6_28·b_6_30·b_1_25
       + a_6_28·b_6_27·b_1_24·b_1_4 + a_6_28·b_6_27·b_1_25 + a_6_20·b_6_30·b_1_24·b_1_4
       + a_6_20·b_6_30·b_1_25 + a_6_20·b_6_27·b_1_24·b_1_4 + a_6_20·b_6_27·b_1_25
       + a_6_20·b_6_30·a_1_1·b_1_24 + a_6_20·b_6_29·a_1_1·b_1_23·b_1_4
       + a_6_20·b_6_29·a_1_1·b_1_24 + a_6_20·b_6_27·a_1_1·b_1_24
       + a_6_20·b_6_27·a_1_0·b_1_24 + a_6_202·b_1_25 + b_6_27·c_8_51·a_1_0·b_1_2·b_1_4
       + b_6_27·c_8_50·a_1_0·b_1_2·b_1_4 + a_6_28·c_8_51·b_1_22·b_1_4
       + a_6_20·c_8_51·b_1_22·b_1_4 + a_6_20·c_8_51·b_1_23 + a_6_20·c_8_50·b_1_22·b_1_4
       + a_6_20·c_8_50·b_1_23 + b_6_27·c_8_51·a_1_0·a_1_1·b_1_4
       + b_6_27·c_8_51·a_1_0·a_1_1·b_1_2 + b_6_27·c_8_51·a_1_02·b_1_4
       + b_6_27·c_8_50·a_1_0·a_1_1·b_1_4 + b_6_27·c_8_50·a_1_0·a_1_1·b_1_2
       + b_6_27·c_8_50·a_1_02·b_1_4 + a_6_28·c_8_51·a_1_1·b_1_2·b_1_4
       + a_6_28·c_8_50·a_1_1·b_1_2·b_1_4 + a_6_20·c_8_51·a_1_1·b_1_3·b_1_4
       + a_6_20·c_8_51·a_1_0·b_1_2·b_1_4 + a_6_20·c_8_51·a_1_0·b_1_22
       + a_6_20·c_8_50·a_1_0·b_1_22 + b_6_27·c_8_51·a_1_02·a_1_1
       + a_6_28·c_8_51·a_1_12·b_1_4 + a_6_28·c_8_51·a_1_0·a_1_1·b_1_4
       + a_6_28·c_8_50·a_1_12·b_1_4 + a_6_28·c_8_50·a_1_0·a_1_1·b_1_4
       + a_6_28·c_8_50·a_1_02·b_1_4 + a_6_20·c_8_51·a_1_12·b_1_2
       + a_6_20·c_8_51·a_1_0·a_1_1·b_1_4 + a_6_20·c_8_51·a_1_02·b_1_2
       + a_6_20·c_8_50·a_1_12·b_1_2 + a_6_20·c_8_50·a_1_0·a_1_1·b_1_4
       + a_6_20·c_8_50·a_1_02·b_1_4 + a_6_20·c_8_50·a_1_02·b_1_2
       + a_6_28·c_8_51·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_03 + a_6_28·c_8_50·a_1_13
       + a_6_28·c_8_50·a_1_02·a_1_1 + a_6_20·c_8_51·a_1_13 + a_6_20·c_8_51·a_1_0·a_1_12
       + a_6_20·c_8_51·a_1_02·a_1_1 + a_6_20·c_8_51·a_1_03 + a_6_20·c_8_50·a_1_13
       + a_6_20·c_8_50·a_1_03
  49. b_6_31·b_11_94 + b_6_312·b_1_35 + b_6_312·a_1_1·b_1_33·b_1_4
       + b_6_30·b_6_31·a_1_1·b_1_33·b_1_4 + b_6_302·a_1_1·b_1_34
       + b_6_27·b_6_29·a_1_1·b_1_23·b_1_4 + a_6_28·b_6_30·b_1_25
       + a_6_28·b_6_27·b_1_24·b_1_4 + a_6_28·b_6_27·b_1_25 + a_6_20·b_6_30·b_1_25
       + a_6_20·b_6_29·b_1_24·b_1_4 + a_6_20·b_6_29·b_1_25 + a_6_20·b_6_27·b_1_24·b_1_4
       + a_6_20·b_6_27·b_1_25 + a_6_20·b_6_30·a_1_1·b_1_24
       + a_6_20·b_6_29·a_1_1·b_1_23·b_1_4 + a_6_20·b_6_29·a_1_1·b_1_24
       + a_6_20·b_6_27·a_1_1·b_1_24 + a_6_20·a_6_28·b_1_25 + b_6_31·c_8_51·b_1_32·b_1_4
       + b_6_31·c_8_50·b_1_32·b_1_4 + b_6_30·c_8_51·b_1_33 + b_6_30·c_8_50·b_1_33
       + b_6_31·c_8_51·a_1_1·b_1_3·b_1_4 + b_6_31·c_8_50·a_1_1·b_1_32
       + b_6_27·c_8_50·a_1_0·b_1_22 + a_6_28·c_8_51·b_1_22·b_1_4 + a_6_20·c_8_51·b_1_23
       + b_6_27·c_8_51·a_1_0·a_1_1·b_1_2 + b_6_27·c_8_50·a_1_0·a_1_1·b_1_2
       + b_6_27·c_8_50·a_1_02·b_1_4 + a_6_28·c_8_51·a_1_1·b_1_2·b_1_4
       + a_6_28·c_8_50·a_1_1·b_1_2·b_1_4 + a_6_20·c_8_51·a_1_0·b_1_2·b_1_4
       + a_6_20·c_8_50·a_1_1·b_1_3·b_1_4 + a_6_20·c_8_50·a_1_1·b_1_22
       + a_6_20·c_8_50·a_1_0·b_1_2·b_1_4 + b_6_27·c_8_51·a_1_02·a_1_1
       + a_6_28·c_8_51·a_1_12·b_1_4 + a_6_20·c_8_51·a_1_12·b_1_4
       + a_6_20·c_8_51·a_1_12·b_1_2 + a_6_20·c_8_51·a_1_0·a_1_1·b_1_4
       + a_6_20·c_8_51·a_1_0·a_1_1·b_1_2 + a_6_20·c_8_51·a_1_02·b_1_4
       + a_6_20·c_8_51·a_1_02·b_1_2 + a_6_20·c_8_50·a_1_12·b_1_4
       + a_6_20·c_8_50·a_1_12·b_1_2 + a_6_20·c_8_50·a_1_0·a_1_1·b_1_4
       + a_6_20·c_8_50·a_1_02·b_1_4 + a_6_28·c_8_51·a_1_13 + a_6_28·c_8_50·a_1_03
       + a_6_20·c_8_51·a_1_13 + a_6_20·c_8_51·a_1_0·a_1_12 + a_6_20·c_8_51·a_1_03
       + a_6_20·c_8_50·a_1_03
  50. b_6_30·b_11_94 + b_6_30·b_6_31·b_1_34·b_1_4 + b_6_30·b_6_31·b_1_35
       + b_6_302·b_1_35 + b_6_292·b_1_25 + b_6_27·b_6_30·b_1_24·b_1_4
       + b_6_27·b_6_29·b_1_25 + b_6_312·a_1_1·b_1_33·b_1_4 + b_6_312·a_1_1·b_1_34
       + b_6_30·b_6_31·a_1_1·b_1_33·b_1_4 + b_6_27·b_6_30·a_1_0·b_1_24
       + b_6_27·b_6_29·a_1_1·b_1_24 + a_6_28·b_6_30·b_1_25 + a_6_28·b_6_27·b_1_25
       + a_6_20·b_6_30·b_1_25 + a_6_20·b_6_27·b_1_24·b_1_4 + a_6_28·b_6_27·a_1_1·b_1_24
       + a_6_20·b_6_29·a_1_1·b_1_23·b_1_4 + a_6_20·b_6_27·a_1_0·b_1_24
       + a_6_20·a_6_28·b_1_25 + b_6_31·c_8_51·b_1_33 + b_6_30·c_8_51·b_1_32·b_1_4
       + b_6_30·c_8_51·b_1_22·b_1_4 + b_6_30·c_8_51·b_1_23 + b_6_30·c_8_50·b_1_32·b_1_4
       + b_6_30·c_8_50·b_1_23 + b_6_29·c_8_50·b_1_23 + b_6_27·c_8_51·b_1_23
       + b_6_27·c_8_50·b_1_23 + c_8_51·a_1_1·b_1_37·b_1_4
       + b_6_30·c_8_51·a_1_1·b_1_3·b_1_4 + b_6_30·c_8_51·a_1_1·b_1_22
       + b_6_30·c_8_50·a_1_1·b_1_32 + b_6_30·c_8_50·a_1_0·b_1_22
       + b_6_29·c_8_50·a_1_1·b_1_22 + b_6_27·c_8_51·a_1_1·b_1_2·b_1_4
       + b_6_27·c_8_51·a_1_1·b_1_22 + b_6_27·c_8_51·a_1_0·b_1_2·b_1_4
       + b_6_27·c_8_50·a_1_1·b_1_2·b_1_4 + b_6_27·c_8_50·a_1_0·b_1_22
       + a_6_28·c_8_51·b_1_23 + a_6_28·c_8_50·b_1_23 + a_6_20·c_8_51·b_1_22·b_1_4
       + a_6_20·c_8_51·b_1_23 + b_6_27·c_8_51·a_1_0·a_1_1·b_1_2
       + b_6_27·c_8_50·a_1_0·a_1_1·b_1_4 + b_6_27·c_8_50·a_1_0·a_1_1·b_1_2
       + b_6_27·c_8_50·a_1_02·b_1_4 + a_6_28·c_8_51·a_1_1·b_1_2·b_1_4
       + a_6_28·c_8_51·a_1_1·b_1_22 + a_6_28·c_8_50·a_1_1·b_1_2·b_1_4
       + a_6_28·c_8_50·a_1_1·b_1_22 + a_6_20·c_8_51·a_1_1·b_1_3·b_1_4
       + a_6_20·c_8_51·a_1_1·b_1_22 + a_6_20·c_8_50·a_1_1·b_1_3·b_1_4
       + a_6_20·c_8_50·a_1_0·b_1_2·b_1_4 + a_6_20·c_8_50·a_1_0·b_1_22
       + a_6_28·c_8_51·a_1_12·b_1_4 + a_6_28·c_8_51·a_1_0·a_1_1·b_1_4
       + a_6_28·c_8_50·a_1_02·b_1_4 + a_6_20·c_8_51·a_1_12·b_1_2
       + a_6_20·c_8_51·a_1_0·a_1_1·b_1_4 + a_6_20·c_8_51·a_1_0·a_1_1·b_1_2
       + a_6_20·c_8_51·a_1_02·b_1_2 + a_6_20·c_8_50·a_1_12·b_1_4
       + a_6_20·c_8_50·a_1_12·b_1_2 + a_6_20·c_8_50·a_1_0·a_1_1·b_1_2
       + a_6_28·c_8_51·a_1_13 + a_6_28·c_8_51·a_1_03 + a_6_28·c_8_50·a_1_13
       + a_6_20·c_8_51·a_1_0·a_1_12 + a_6_20·c_8_51·a_1_02·a_1_1 + a_6_20·c_8_50·a_1_13
       + a_6_20·c_8_50·a_1_0·a_1_12 + a_6_20·c_8_50·a_1_03
  51. b_6_27·b_6_29·a_1_1·b_1_23·b_1_4 + a_6_28·b_6_27·b_1_24·b_1_4
       + a_6_28·b_6_27·b_1_25 + a_6_20·b_11_94 + a_6_20·b_6_30·b_1_25
       + a_6_20·b_6_27·b_1_24·b_1_4 + a_6_20·b_6_27·b_1_25 + a_6_28·b_6_27·a_1_1·b_1_24
       + a_6_20·b_6_29·a_1_1·b_1_23·b_1_4 + a_6_20·b_6_27·a_1_1·b_1_24
       + a_6_20·a_6_28·b_1_25 + a_6_202·b_1_25 + a_6_28·c_8_50·b_1_23
       + a_6_20·c_8_51·b_1_22·b_1_4 + b_6_27·c_8_51·a_1_0·a_1_1·b_1_2
       + b_6_27·c_8_51·a_1_02·b_1_4 + b_6_27·c_8_50·a_1_0·a_1_1·b_1_2
       + b_6_27·c_8_50·a_1_02·b_1_4 + a_6_28·c_8_50·a_1_1·b_1_22
       + a_6_20·c_8_51·a_1_1·b_1_3·b_1_4 + a_6_20·c_8_51·a_1_1·b_1_2·b_1_4
       + a_6_20·c_8_51·a_1_1·b_1_22 + a_6_20·c_8_51·a_1_0·b_1_2·b_1_4
       + a_6_20·c_8_50·a_1_1·b_1_2·b_1_4 + a_6_20·c_8_50·a_1_1·b_1_22
       + b_6_27·c_8_51·a_1_02·a_1_1 + a_6_28·c_8_51·a_1_12·b_1_4
       + a_6_28·c_8_51·a_1_0·a_1_1·b_1_4 + a_6_28·c_8_50·a_1_02·b_1_4
       + a_6_20·c_8_51·a_1_12·b_1_4 + a_6_20·c_8_51·a_1_12·b_1_2
       + a_6_20·c_8_51·a_1_02·b_1_4 + a_6_20·c_8_50·a_1_0·a_1_1·b_1_2
       + a_6_20·c_8_50·a_1_02·b_1_4 + a_6_28·c_8_50·a_1_03 + a_6_20·c_8_51·a_1_13
       + a_6_20·c_8_51·a_1_02·a_1_1 + a_6_20·c_8_51·a_1_03 + a_6_20·c_8_50·a_1_0·a_1_12
       + a_6_20·c_8_50·a_1_02·a_1_1
  52. b_11_932 + b_6_313·b_1_34 + b_6_302·b_1_310 + b_6_292·b_6_30·b_1_24
       + b_6_30·b_6_312·a_1_1·b_1_33 + b_6_272·b_6_30·a_1_1·b_1_23
       + b_6_272·b_6_29·a_1_1·b_1_23 + a_6_28·b_6_29·b_6_30·b_1_24
       + a_6_28·b_6_292·b_1_24 + a_6_28·b_6_27·b_6_29·b_1_24
       + a_6_20·b_6_29·b_6_30·b_1_23·b_1_4 + a_6_20·b_6_29·b_6_30·b_1_24
       + a_6_20·b_6_27·b_6_29·b_1_23·b_1_4 + a_6_20·b_6_27·b_6_29·b_1_24
       + a_6_20·b_6_272·b_1_24 + a_6_20·b_6_29·b_6_30·a_1_1·b_1_23
       + a_6_20·b_6_27·b_6_29·a_1_1·b_1_23 + a_6_20·b_6_272·a_1_1·b_1_23
       + a_6_202·b_6_30·b_1_24 + a_6_202·b_6_29·b_1_24 + b_6_312·c_8_51·b_1_32
       + b_6_312·c_8_50·b_1_32 + b_6_292·c_8_51·b_1_22 + b_6_272·c_8_51·b_1_22
       + b_6_272·c_8_50·b_1_22 + b_6_29·b_6_30·c_8_50·a_1_1·b_1_2
       + b_6_27·b_6_30·c_8_51·a_1_1·b_1_2 + b_6_27·b_6_30·c_8_51·a_1_0·b_1_2
       + b_6_27·b_6_30·c_8_50·a_1_1·b_1_2 + b_6_27·b_6_29·c_8_50·a_1_1·b_1_2
       + b_6_272·c_8_50·a_1_1·b_1_2 + a_6_28·b_6_27·c_8_51·b_1_2·b_1_4
       + a_6_28·b_6_27·c_8_50·b_1_2·b_1_4 + a_6_20·b_6_30·c_8_51·b_1_22
       + a_6_20·b_6_30·c_8_50·b_1_2·b_1_4 + a_6_20·b_6_29·c_8_51·b_1_2·b_1_4
       + a_6_20·b_6_29·c_8_50·b_1_2·b_1_4 + a_6_20·b_6_27·c_8_51·b_1_2·b_1_4
       + a_6_28·b_6_27·c_8_51·a_1_1·b_1_2 + a_6_28·b_6_27·c_8_50·a_1_1·b_1_2
       + a_6_20·b_6_30·c_8_50·a_1_1·b_1_2 + a_6_20·b_6_29·c_8_50·a_1_1·b_1_2
       + a_6_20·b_6_27·c_8_51·a_1_1·b_1_2 + a_6_20·b_6_27·c_8_50·a_1_0·b_1_2
       + a_6_20·a_6_28·c_8_51·b_1_22 + c_8_512·b_1_36 + c_8_50·c_8_51·b_1_26
       + c_8_502·b_1_26 + c_8_50·c_8_51·a_1_1·b_1_25
       + c_8_50·c_8_51·a_1_0·b_1_24·b_1_4 + c_8_502·a_1_0·b_1_24·b_1_4
       + c_8_50·c_8_51·a_1_0·a_1_1·b_1_23·b_1_4 + c_8_50·c_8_51·a_1_0·a_1_1·b_1_24
       + c_8_512·a_1_04·b_1_2·b_1_4 + c_8_50·c_8_51·a_1_0·a_1_13·b_1_2·b_1_4
       + c_8_50·c_8_51·a_1_03·a_1_1·b_1_3·b_1_4 + c_8_50·c_8_51·a_1_03·a_1_1·b_1_2·b_1_4
       + c_8_50·c_8_51·a_1_04·b_1_2·b_1_4 + c_8_502·a_1_0·a_1_13·b_1_2·b_1_4
       + c_8_502·a_1_03·a_1_1·b_1_2·b_1_4 + c_8_502·a_1_04·b_1_2·b_1_4
       + c_8_512·a_1_15·b_1_4 + c_8_512·a_1_04·a_1_1·b_1_3
       + c_8_512·a_1_04·a_1_1·b_1_2 + c_8_50·c_8_51·a_1_04·a_1_1·b_1_2
       + c_8_50·c_8_51·a_1_05·b_1_4 + c_8_502·a_1_02·a_1_13·b_1_4
       + c_8_502·a_1_04·a_1_1·b_1_2 + c_8_502·a_1_05·b_1_4 + c_8_512·a_1_0·a_1_15
       + c_8_512·a_1_05·a_1_1 + c_8_502·a_1_0·a_1_15 + c_8_502·a_1_05·a_1_1
  53. b_11_93·b_11_94 + b_6_313·b_1_33·b_1_4 + b_6_313·b_1_34
       + b_6_30·b_6_312·b_1_34 + b_6_302·b_1_310 + b_6_292·b_6_30·b_1_24
       + b_6_27·b_6_29·b_6_30·b_1_23·b_1_4 + b_6_27·b_6_29·b_6_30·b_1_24
       + b_6_272·b_6_29·b_1_24 + b_6_273·b_1_24 + b_6_313·a_1_1·b_1_32·b_1_4
       + b_6_313·a_1_1·b_1_33 + b_6_302·a_1_1·b_1_39
       + b_6_27·b_6_29·b_6_30·a_1_1·b_1_23 + b_6_272·b_6_29·a_1_1·b_1_23
       + a_6_28·b_6_27·b_6_30·b_1_24 + a_6_28·b_6_27·b_6_29·b_1_24
       + a_6_20·b_6_27·b_6_30·b_1_23·b_1_4 + a_6_20·b_6_27·b_6_30·b_1_24
       + a_6_20·b_6_27·b_6_29·b_1_23·b_1_4 + a_6_20·b_6_27·b_6_29·b_1_24
       + a_6_20·b_6_272·b_1_24 + a_6_20·b_6_29·b_6_30·a_1_1·b_1_23
       + a_6_20·b_6_272·a_1_1·b_1_23 + a_6_20·a_6_28·b_6_27·b_1_24
       + a_6_202·b_6_30·b_1_24 + c_8_51·b_1_313·b_1_4 + b_6_312·c_8_51·b_1_3·b_1_4
       + b_6_312·c_8_50·b_1_3·b_1_4 + b_6_30·c_8_50·b_1_38
       + b_6_30·b_6_31·c_8_50·b_1_3·b_1_4 + b_6_30·b_6_31·c_8_50·b_1_32
       + b_6_302·c_8_50·b_1_32 + b_6_29·b_6_30·c_8_51·b_1_2·b_1_4
       + b_6_29·b_6_30·c_8_51·b_1_22 + b_6_29·b_6_30·c_8_50·b_1_22
       + b_6_292·c_8_51·b_1_22 + b_6_292·c_8_50·b_1_22 + b_6_27·b_6_30·c_8_50·b_1_22
       + c_8_51·a_1_1·b_1_312·b_1_4 + c_8_50·a_1_1·b_1_312·b_1_4
       + b_6_312·c_8_51·a_1_1·b_1_4 + b_6_312·c_8_50·a_1_1·b_1_4
       + b_6_312·c_8_50·a_1_1·b_1_3 + b_6_30·c_8_50·a_1_1·b_1_37
       + b_6_30·b_6_31·c_8_51·a_1_1·b_1_4 + b_6_30·b_6_31·c_8_50·a_1_1·b_1_4
       + b_6_302·c_8_51·a_1_1·b_1_3 + b_6_29·b_6_30·c_8_51·a_1_1·b_1_2
       + b_6_29·b_6_30·c_8_50·a_1_1·b_1_2 + b_6_272·c_8_51·a_1_1·b_1_2
       + a_6_28·b_6_30·c_8_51·b_1_22 + a_6_28·b_6_30·c_8_50·b_1_22
       + a_6_28·b_6_29·c_8_51·b_1_22 + a_6_28·b_6_29·c_8_50·b_1_22
       + a_6_28·b_6_27·c_8_51·b_1_22 + a_6_20·b_6_29·c_8_51·b_1_22
       + a_6_20·b_6_29·c_8_50·b_1_2·b_1_4 + a_6_20·b_6_27·c_8_51·b_1_22
       + a_6_28·b_6_27·c_8_51·a_1_1·b_1_2 + a_6_20·b_6_30·c_8_50·a_1_1·b_1_2
       + a_6_20·b_6_29·c_8_50·a_1_1·b_1_2 + a_6_20·b_6_27·c_8_51·a_1_1·b_1_2
       + a_6_20·b_6_27·c_8_50·a_1_1·b_1_2 + a_6_20·b_6_27·c_8_50·a_1_0·b_1_2
       + a_6_20·a_6_28·c_8_51·b_1_22 + a_6_20·a_6_28·c_8_50·b_1_22
       + c_8_512·b_1_35·b_1_4 + c_8_512·b_1_25·b_1_4 + c_8_512·b_1_26
       + c_8_50·c_8_51·b_1_35·b_1_4 + c_8_50·c_8_51·b_1_36 + c_8_50·c_8_51·b_1_25·b_1_4
       + c_8_50·c_8_51·b_1_26 + c_8_502·b_1_26 + c_8_512·a_1_1·b_1_34·b_1_4
       + c_8_512·a_1_1·b_1_35 + c_8_512·a_1_1·b_1_24·b_1_4 + c_8_512·a_1_0·b_1_25
       + c_8_50·c_8_51·a_1_1·b_1_34·b_1_4 + c_8_50·c_8_51·a_1_1·b_1_35
       + c_8_50·c_8_51·a_1_1·b_1_24·b_1_4 + c_8_50·c_8_51·a_1_1·b_1_25
       + c_8_50·c_8_51·a_1_0·b_1_25 + c_8_502·a_1_1·b_1_24·b_1_4
       + c_8_512·a_1_0·a_1_1·b_1_23·b_1_4 + c_8_50·c_8_51·a_1_0·a_1_1·b_1_23·b_1_4
       + c_8_512·a_1_04·b_1_2·b_1_4 + c_8_50·c_8_51·a_1_0·a_1_13·b_1_2·b_1_4
       + c_8_50·c_8_51·a_1_03·a_1_1·b_1_3·b_1_4 + c_8_50·c_8_51·a_1_03·a_1_1·b_1_2·b_1_4
       + c_8_50·c_8_51·a_1_04·b_1_2·b_1_4 + c_8_502·a_1_0·a_1_13·b_1_2·b_1_4
       + c_8_502·a_1_03·a_1_1·b_1_3·b_1_4 + c_8_502·a_1_03·a_1_1·b_1_2·b_1_4
       + c_8_512·a_1_15·b_1_4 + c_8_512·a_1_0·a_1_14·b_1_4
       + c_8_512·a_1_04·a_1_1·b_1_4 + c_8_512·a_1_04·a_1_1·b_1_3
       + c_8_512·a_1_04·a_1_1·b_1_2 + c_8_50·c_8_51·a_1_15·b_1_4
       + c_8_50·c_8_51·a_1_04·a_1_1·b_1_4 + c_8_502·a_1_04·a_1_1·b_1_4
       + c_8_502·a_1_04·a_1_1·b_1_3 + c_8_502·a_1_04·a_1_1·b_1_2
       + c_8_502·a_1_05·b_1_4 + c_8_512·a_1_0·a_1_15 + c_8_512·a_1_05·a_1_1
       + c_8_502·a_1_0·a_1_15 + c_8_502·a_1_05·a_1_1
  54. b_11_942 + b_6_313·b_1_34 + b_6_302·b_1_310 + b_6_302·b_6_31·b_1_34
       + b_6_292·b_6_30·b_1_24 + b_6_272·b_6_30·b_1_24
       + b_6_30·b_6_312·a_1_1·b_1_33 + b_6_27·b_6_29·b_6_30·a_1_1·b_1_23
       + b_6_272·b_6_30·a_1_1·b_1_23 + a_6_28·b_6_29·b_6_30·b_1_24
       + a_6_28·b_6_292·b_1_24 + a_6_28·b_6_27·b_6_30·b_1_24
       + a_6_20·b_6_29·b_6_30·b_1_24 + a_6_20·b_6_292·b_1_24
       + a_6_20·b_6_27·b_6_30·b_1_23·b_1_4 + a_6_20·b_6_27·b_6_29·b_1_24
       + a_6_20·b_6_27·b_6_29·a_1_1·b_1_23 + a_6_20·a_6_28·b_6_27·b_1_24
       + a_6_202·b_6_30·b_1_24 + b_6_312·c_8_51·b_1_32 + b_6_312·c_8_50·b_1_32
       + b_6_302·c_8_51·b_1_32 + b_6_302·c_8_50·b_1_32 + b_6_292·c_8_51·b_1_22
       + b_6_292·c_8_50·b_1_22 + b_6_27·b_6_30·c_8_51·b_1_2·b_1_4
       + b_6_27·b_6_30·c_8_51·b_1_22 + b_6_272·c_8_51·b_1_22 + b_6_272·c_8_50·b_1_22
       + c_8_51·a_1_1·b_1_312·b_1_4 + b_6_30·c_8_51·a_1_1·b_1_37
       + b_6_29·b_6_30·c_8_51·a_1_1·b_1_2 + b_6_29·b_6_30·c_8_50·a_1_1·b_1_2
       + b_6_27·b_6_30·c_8_51·a_1_1·b_1_2 + b_6_27·b_6_30·c_8_51·a_1_0·b_1_2
       + b_6_27·b_6_30·c_8_50·a_1_1·b_1_2 + b_6_27·b_6_30·c_8_50·a_1_0·b_1_2
       + b_6_27·b_6_29·c_8_51·a_1_1·b_1_2 + b_6_27·b_6_29·c_8_50·a_1_1·b_1_2
       + b_6_272·c_8_51·a_1_1·b_1_2 + b_6_272·c_8_50·a_1_1·b_1_2
       + a_6_20·b_6_29·c_8_51·b_1_2·b_1_4 + a_6_20·b_6_29·c_8_51·b_1_22
       + a_6_20·b_6_27·c_8_51·b_1_2·b_1_4 + a_6_20·b_6_27·c_8_50·b_1_2·b_1_4
       + a_6_20·b_6_27·c_8_50·b_1_22 + a_6_28·b_6_27·c_8_50·a_1_1·b_1_2
       + a_6_20·b_6_30·c_8_51·a_1_1·b_1_2 + a_6_20·b_6_29·c_8_50·a_1_1·b_1_2
       + a_6_20·b_6_27·c_8_51·a_1_0·b_1_2 + a_6_20·b_6_27·c_8_50·a_1_1·b_1_2
       + a_6_20·b_6_27·c_8_50·a_1_0·b_1_2 + a_6_20·a_6_28·c_8_50·b_1_22
       + c_8_512·b_1_36 + c_8_512·b_1_25·b_1_4 + c_8_512·b_1_26
       + c_8_50·c_8_51·b_1_25·b_1_4 + c_8_50·c_8_51·b_1_26 + c_8_502·b_1_36
       + c_8_502·b_1_26 + c_8_512·a_1_1·b_1_24·b_1_4 + c_8_512·a_1_0·b_1_24·b_1_4
       + c_8_502·a_1_0·b_1_24·b_1_4 + c_8_512·a_1_0·a_1_1·b_1_23·b_1_4
       + c_8_512·a_1_0·a_1_1·b_1_24 + c_8_502·a_1_0·a_1_1·b_1_24
       + c_8_512·a_1_04·b_1_3·b_1_4 + c_8_512·a_1_04·b_1_2·b_1_4
       + c_8_50·c_8_51·a_1_0·a_1_13·b_1_2·b_1_4 + c_8_50·c_8_51·a_1_03·a_1_1·b_1_2·b_1_4
       + c_8_50·c_8_51·a_1_04·b_1_2·b_1_4 + c_8_502·a_1_03·a_1_1·b_1_2·b_1_4
       + c_8_502·a_1_04·b_1_3·b_1_4 + c_8_502·a_1_04·b_1_2·b_1_4
       + c_8_512·a_1_0·a_1_14·b_1_4 + c_8_512·a_1_04·a_1_1·b_1_4
       + c_8_512·a_1_04·a_1_1·b_1_3 + c_8_512·a_1_05·b_1_4
       + c_8_50·c_8_51·a_1_04·a_1_1·b_1_4 + c_8_50·c_8_51·a_1_04·a_1_1·b_1_2
       + c_8_502·a_1_15·b_1_4 + c_8_502·a_1_04·a_1_1·b_1_4 + c_8_512·a_1_0·a_1_15
       + c_8_50·c_8_51·a_1_0·a_1_15 + c_8_502·a_1_0·a_1_15 + c_8_502·a_1_05·a_1_1

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 22.
  • 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_8_50, a Duflot regular element of degree 8
    2. c_8_51, a Duflot regular element of degree 8
    3. b_1_32 + b_1_22, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 12, 15].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].

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 2

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_1_3 → 0, an element of degree 1
  5. b_1_4 → 0, an element of degree 1
  6. a_6_20 → 0, an element of degree 6
  7. a_6_28 → 0, an element of degree 6
  8. b_6_27 → 0, an element of degree 6
  9. b_6_29 → 0, an element of degree 6
  10. b_6_30 → 0, an element of degree 6
  11. b_6_31 → 0, an element of degree 6
  12. c_8_50 → c_1_18 + c_1_08, an element of degree 8
  13. c_8_51 → c_1_08, an element of degree 8
  14. b_11_93 → 0, an element of degree 11
  15. b_11_94 → 0, an element of degree 11

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

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_1_3 → c_1_2, an element of degree 1
  5. b_1_4 → 0, an element of degree 1
  6. a_6_20 → 0, an element of degree 6
  7. a_6_28 → 0, an element of degree 6
  8. b_6_27 → 0, an element of degree 6
  9. b_6_29 → 0, an element of degree 6
  10. b_6_30 → c_1_02·c_1_24 + c_1_04·c_1_22, an element of degree 6
  11. b_6_31 → c_1_12·c_1_24 + c_1_14·c_1_22, an element of degree 6
  12. c_8_50 → c_1_12·c_1_26 + c_1_18 + c_1_04·c_1_24 + c_1_08, an element of degree 8
  13. c_8_51 → c_1_04·c_1_24 + c_1_08, an element of degree 8
  14. b_11_93 → c_1_14·c_1_27 + c_1_18·c_1_23 + c_1_02·c_1_29 + c_1_08·c_1_23, an element of degree 11
  15. b_11_94 → c_1_12·c_1_29 + c_1_14·c_1_27 + c_1_02·c_1_29 + c_1_02·c_1_12·c_1_27
       + c_1_02·c_1_14·c_1_25 + c_1_04·c_1_27 + c_1_04·c_1_12·c_1_25
       + c_1_04·c_1_14·c_1_23, an element of degree 11

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

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. b_1_2 → c_1_2, an element of degree 1
  4. b_1_3 → 0, an element of degree 1
  5. b_1_4 → 0, an element of degree 1
  6. a_6_20 → 0, an element of degree 6
  7. a_6_28 → 0, an element of degree 6
  8. b_6_27 → c_1_12·c_1_24 + c_1_14·c_1_22 + c_1_02·c_1_24 + c_1_04·c_1_22, an element of degree 6
  9. b_6_29 → c_1_12·c_1_24 + c_1_14·c_1_22, an element of degree 6
  10. b_6_30 → c_1_26 + c_1_12·c_1_24 + c_1_14·c_1_22 + c_1_02·c_1_24 + c_1_04·c_1_22, an element of degree 6
  11. b_6_31 → 0, an element of degree 6
  12. c_8_50 → c_1_28 + c_1_12·c_1_26 + c_1_18 + c_1_02·c_1_26 + c_1_08, an element of degree 8
  13. c_8_51 → c_1_04·c_1_24 + c_1_08, an element of degree 8
  14. b_11_93 → c_1_211 + c_1_12·c_1_29 + c_1_14·c_1_27 + c_1_02·c_1_29
       + c_1_02·c_1_12·c_1_27 + c_1_02·c_1_14·c_1_25 + c_1_04·c_1_27
       + c_1_04·c_1_12·c_1_25 + c_1_04·c_1_14·c_1_23, an element of degree 11
  15. b_11_94 → c_1_211 + c_1_12·c_1_29 + c_1_18·c_1_23 + c_1_02·c_1_12·c_1_27
       + c_1_02·c_1_14·c_1_25 + c_1_04·c_1_12·c_1_25 + c_1_04·c_1_14·c_1_23, an element of degree 11

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

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. b_1_2 → c_1_2, an element of degree 1
  4. b_1_3 → 0, an element of degree 1
  5. b_1_4 → c_1_2, an element of degree 1
  6. a_6_20 → 0, an element of degree 6
  7. a_6_28 → 0, an element of degree 6
  8. b_6_27 → c_1_26 + c_1_12·c_1_24 + c_1_14·c_1_22 + c_1_02·c_1_24 + c_1_04·c_1_22, an element of degree 6
  9. b_6_29 → c_1_26 + c_1_12·c_1_24 + c_1_14·c_1_22, an element of degree 6
  10. b_6_30 → c_1_12·c_1_24 + c_1_14·c_1_22 + c_1_02·c_1_24 + c_1_04·c_1_22, an element of degree 6
  11. b_6_31 → 0, an element of degree 6
  12. c_8_50 → c_1_28 + c_1_14·c_1_24 + c_1_18 + c_1_04·c_1_24 + c_1_08, an element of degree 8
  13. c_8_51 → c_1_12·c_1_26 + c_1_14·c_1_24 + c_1_02·c_1_26 + c_1_08, an element of degree 8
  14. b_11_93 → c_1_02·c_1_29 + c_1_02·c_1_12·c_1_27 + c_1_02·c_1_14·c_1_25
       + c_1_04·c_1_27 + c_1_04·c_1_12·c_1_25 + c_1_04·c_1_14·c_1_23, an element of degree 11
  15. b_11_94 → c_1_211 + c_1_14·c_1_27 + c_1_18·c_1_23 + c_1_02·c_1_29
       + c_1_02·c_1_12·c_1_27 + c_1_02·c_1_14·c_1_25 + c_1_04·c_1_12·c_1_25
       + c_1_04·c_1_14·c_1_23 + c_1_08·c_1_23, an element of degree 11

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