Cohomology of group number 516 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 4.
  • Its center has rank 2.
  • It has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 4.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    t6  −  t5  +  3·t4  −  3·t3  +  3·t2  −  t  +  1
    (t  −  1)4 · (t2  +  1) · (t4  +  1)
  • The a-invariants are -∞,-∞,-4,-4,-4. 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 18 minimal generators of maximal degree 8:

  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. a_2_4, a nilpotent element of degree 2
  6. b_2_5, an element of degree 2
  7. b_2_6, an element of degree 2
  8. c_2_7, a Duflot regular element of degree 2
  9. a_3_10, a nilpotent element of degree 3
  10. a_3_15, a nilpotent element of degree 3
  11. a_5_37, a nilpotent element of degree 5
  12. b_5_40, an element of degree 5
  13. b_5_41, an element of degree 5
  14. a_6_57, a nilpotent element of degree 6
  15. a_6_48, a nilpotent element of degree 6
  16. b_6_60, an element of degree 6
  17. a_7_71, a nilpotent element of degree 7
  18. c_8_124, a Duflot regular element of degree 8

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

Ring relations

There are 103 minimal relations of maximal degree 14:

  1. a_1_02
  2. a_1_0·a_1_1
  3. a_1_0·b_1_2
  4. a_2_3·a_1_0
  5. a_2_3·b_1_2 + a_2_4·a_1_1
  6. a_2_4·a_1_0
  7. b_2_5·a_1_0
  8. b_2_6·a_1_0 + a_1_13
  9. a_2_32 + a_2_3·a_1_12
  10. a_1_12·b_1_22 + a_2_4·a_1_1·b_1_2 + a_2_42
  11. a_2_3·a_2_4 + a_2_4·a_1_12
  12. b_2_6·b_1_22 + b_2_52 + b_2_5·a_1_1·b_1_2 + c_2_7·a_1_12
  13. b_1_2·a_3_10 + a_2_4·b_2_5
  14. a_2_3·b_2_5 + a_1_1·a_3_10
  15. a_1_0·a_3_10
  16. b_1_2·a_3_15 + a_2_4·b_2_6 + b_2_5·a_1_12
  17. a_2_3·b_2_6 + a_1_1·a_3_15
  18. a_1_0·a_3_15 + a_2_32
  19. b_2_6·a_1_13
  20. b_2_5·a_3_10 + a_2_4·b_2_6·b_1_2 + a_2_4·b_2_5·a_1_1 + a_2_3·c_2_7·a_1_1
  21. b_2_5·a_1_12·b_1_2 + a_2_4·a_3_10 + a_2_4·b_2_5·a_1_1
  22. a_2_3·a_3_10 + a_1_12·a_3_10
  23. b_2_6·a_3_10 + b_2_5·a_3_15 + b_2_6·a_1_12·b_1_2
  24. b_2_6·a_1_12·b_1_2 + a_2_4·a_3_15 + a_2_4·b_2_6·a_1_1 + a_2_3·a_3_10
  25. a_2_3·a_3_15 + a_1_12·a_3_15
  26. a_3_102 + a_2_42·b_2_6 + a_2_4·b_2_5·a_1_12 + a_2_3·c_2_7·a_1_12
  27. a_3_10·a_3_15 + b_2_5·a_1_1·a_3_15 + b_2_5·b_2_6·a_1_12 + a_2_4·b_2_6·a_1_12
  28. a_3_152 + b_2_6·a_1_1·a_3_15 + b_2_62·a_1_12 + a_1_13·a_3_15
  29. b_1_2·a_5_37 + b_2_5·b_2_6·a_1_12
  30. a_1_1·a_5_37
  31. a_1_0·a_5_37 + a_1_13·a_3_15
  32. a_1_0·b_5_40 + a_1_13·a_3_15
  33. b_1_2·b_5_40 + b_2_5·b_2_62 + a_1_1·b_5_41
  34. a_1_0·b_5_41
  35. b_2_5·a_5_37 + a_2_4·b_2_6·a_3_15 + a_2_4·b_2_62·a_1_1 + b_2_5·a_1_12·a_3_15
  36. a_2_3·a_5_37
  37. a_2_4·a_5_37 + b_2_5·a_1_12·a_3_15
  38. b_2_6·a_5_37 + a_1_12·b_5_40
  39. b_2_5·b_2_6·a_3_15 + a_2_4·b_5_40 + a_2_3·b_5_41 + a_2_4·b_2_6·a_3_15
       + a_2_4·b_2_62·a_1_1 + b_2_5·a_1_12·a_3_15
  40. a_6_57·b_1_2 + a_2_4·b_5_40 + a_2_4·b_2_6·a_3_15
  41. a_2_3·b_5_40 + a_6_57·a_1_1 + b_2_6·a_1_12·a_3_15
  42. a_6_57·a_1_0
  43. a_1_1·b_1_2·b_5_41 + a_6_48·b_1_2 + b_2_52·b_2_6·a_1_1 + a_2_4·b_5_41
       + a_2_4·b_2_5·b_2_6·a_1_1
  44. b_2_5·b_2_6·a_3_15 + a_2_4·b_5_40 + a_1_12·b_5_41 + a_6_48·a_1_1 + b_2_5·a_1_12·a_3_15
  45. a_6_48·a_1_0
  46. b_6_60·b_1_2 + b_2_5·b_5_41 + b_2_52·b_2_6·a_1_1 + a_2_4·b_5_41 + a_2_4·b_2_5·a_3_15
       + a_2_42·b_2_6·a_1_1 + b_2_62·c_2_7·a_1_1
  47. b_2_63·b_1_2 + b_2_5·b_5_40 + b_6_60·a_1_1 + b_2_5·b_2_6·a_3_15 + b_2_5·b_2_62·a_1_1
       + a_2_4·b_5_40 + b_2_5·a_1_12·a_3_15
  48. b_6_60·a_1_0
  49. a_3_10·a_5_37 + a_2_4·b_2_62·a_1_12
  50. a_3_15·b_5_40 + b_2_6·a_6_57 + a_3_15·a_5_37 + b_2_62·a_1_1·a_3_15
  51. a_3_15·a_5_37 + a_2_3·a_6_57
  52. b_2_5·b_2_62·a_1_12 + a_2_4·a_1_1·b_5_40 + a_2_4·a_6_57
  53. a_3_15·a_5_37 + a_6_57·a_1_12
  54. a_3_10·b_5_41 + b_2_5·a_1_1·b_5_41 + b_2_5·a_6_48 + b_2_5·b_2_62·a_1_1·b_1_2
       + a_2_42·b_2_62 + a_2_4·b_2_5·b_2_6·a_1_12 + c_2_7·a_1_13·a_3_15
  55. a_3_15·b_5_41 + a_3_10·b_5_40 + b_2_6·a_1_1·b_5_41 + b_2_6·a_6_48 + b_2_5·a_1_1·b_5_40
       + b_2_5·a_6_57 + b_2_5·b_2_62·a_1_12 + a_2_4·b_2_62·a_1_12
  56. a_2_3·a_6_48 + a_2_4·b_2_62·a_1_12
  57. a_6_48·a_1_1·b_1_2 + a_2_4·a_1_1·b_5_41 + a_2_4·a_6_48 + a_2_42·b_2_62
       + a_2_4·b_2_5·b_2_6·a_1_12
  58. a_3_10·b_5_40 + b_2_5·a_6_57 + b_2_5·b_2_62·a_1_12 + a_2_4·a_1_1·b_5_40
       + a_6_48·a_1_12 + a_2_4·b_2_62·a_1_12
  59. b_2_6·b_1_2·b_5_41 + b_2_5·b_6_60 + a_3_10·b_5_41 + b_2_5·a_1_1·b_5_41
       + b_2_5·b_2_62·a_1_1·b_1_2 + a_2_4·b_2_62·a_1_1·b_1_2 + a_2_4·b_2_5·b_2_6·a_1_12
       + c_2_7·a_1_1·b_5_40 + c_2_7·a_1_13·a_3_15
  60. a_3_10·b_5_40 + a_2_4·b_2_63 + a_2_3·b_6_60 + a_2_4·a_1_1·b_5_40
       + a_2_4·b_2_62·a_1_12
  61. a_3_10·b_5_41 + a_2_4·b_6_60 + a_6_48·a_1_1·b_1_2 + a_2_42·b_2_62
       + b_2_6·c_2_7·a_1_1·a_3_15 + c_2_7·a_1_13·a_3_15
  62. a_3_10·b_5_41 + b_1_2·a_7_71 + b_2_5·a_1_1·b_5_41 + b_2_5·b_2_62·a_1_1·b_1_2
       + a_6_48·a_1_1·b_1_2 + a_2_4·a_1_1·b_5_41 + a_2_4·b_2_62·a_1_1·b_1_2
       + a_2_42·b_2_62 + a_2_4·b_2_5·b_2_6·a_1_12 + b_2_6·c_2_7·a_1_1·a_3_15
       + b_2_62·c_2_7·a_1_12 + c_2_7·a_1_13·a_3_15
  63. a_3_10·b_5_40 + a_2_4·b_2_63 + a_1_1·a_7_71 + b_6_60·a_1_12 + b_2_5·b_2_62·a_1_12
       + a_2_4·a_1_1·b_5_40
  64. a_1_0·a_7_71
  65. a_6_57·a_3_15 + b_2_6·a_1_12·b_5_40 + b_2_6·a_6_57·a_1_1
  66. a_6_48·a_3_15 + a_6_57·a_3_10 + b_2_6·a_1_12·b_5_41 + a_2_4·b_2_62·a_3_15
       + a_2_4·b_2_63·a_1_1
  67. a_6_48·a_3_10 + b_2_5·a_6_48·a_1_1 + a_2_4·b_6_60·a_1_1 + a_2_42·b_5_40
       + b_2_6·c_2_7·a_1_12·a_3_15
  68. b_6_60·a_3_10 + a_2_4·b_2_6·b_5_41 + a_6_48·a_3_10 + a_2_42·b_2_62·a_1_1
       + c_2_7·a_6_57·a_1_1 + b_2_6·c_2_7·a_1_12·a_3_15
  69. b_2_5·a_7_71 + b_2_5·b_6_60·a_1_1 + b_2_52·b_2_62·a_1_1 + a_2_4·b_2_6·b_5_41
       + a_6_48·a_3_10 + a_2_42·b_5_40 + a_2_4·a_1_12·b_5_41 + a_2_42·b_2_62·a_1_1
       + c_2_7·a_6_57·a_1_1 + b_2_6·c_2_7·a_1_12·a_3_15
  70. b_6_60·a_3_15 + b_2_6·a_7_71 + b_2_6·b_6_60·a_1_1 + b_2_5·b_2_63·a_1_1 + a_6_57·a_3_10
       + b_2_6·a_1_12·b_5_41 + a_2_4·a_6_57·a_1_1
  71. a_2_3·a_7_71 + a_2_4·a_6_57·a_1_1
  72. a_6_48·a_3_10 + a_2_4·a_7_71 + a_2_4·a_1_12·b_5_41
  73. a_6_57·a_3_10 + a_2_4·b_2_62·a_3_15 + a_1_12·a_7_71
  74. a_5_372
  75. a_5_37·b_5_40 + b_2_64·a_1_12
  76. a_5_37·b_5_41 + b_2_6·b_6_60·a_1_12 + b_2_6·a_6_48·a_1_12
  77. a_3_10·a_7_71 + a_2_4·b_2_6·a_6_48 + a_2_4·b_6_60·a_1_12 + a_2_42·a_1_1·b_5_40
  78. a_5_37·b_5_41 + a_3_15·a_7_71 + a_2_4·b_2_6·a_1_1·b_5_40 + b_2_6·a_6_48·a_1_12
  79. b_5_412 + b_2_5·b_2_6·b_6_60 + b_2_52·b_2_63 + b_2_5·b_2_6·a_6_48
       + b_2_52·a_1_1·b_5_40 + a_2_4·b_2_5·a_1_1·b_5_40 + a_2_42·b_2_63
       + a_2_4·b_6_60·a_1_12 + a_2_42·a_1_1·b_5_40 + c_8_124·b_1_22 + b_2_64·c_2_7
       + b_2_6·c_2_7·a_1_1·b_5_40 + b_2_63·c_2_7·a_1_12
  80. b_5_40·b_5_41 + b_2_62·b_6_60 + a_5_37·b_5_41 + b_2_62·a_6_48
       + b_2_5·b_2_6·a_1_1·b_5_40 + c_8_124·a_1_1·b_1_2
  81. b_5_402 + b_2_65 + b_2_62·a_1_1·b_5_40 + b_2_64·a_1_12 + c_8_124·a_1_12
  82. a_6_57·a_5_37 + b_2_63·a_1_12·a_3_15
  83. b_6_60·a_5_37 + a_6_48·a_5_37 + b_2_62·a_1_12·b_5_41
  84. a_6_48·a_5_37 + b_2_6·a_1_12·a_7_71
  85. a_6_48·b_5_40 + a_6_57·b_5_41 + b_2_62·b_6_60·a_1_1 + b_2_5·b_2_64·a_1_1
       + b_2_62·a_1_12·b_5_41 + a_2_4·b_2_63·a_3_15 + a_2_4·b_2_6·a_6_57·a_1_1
       + c_8_124·a_1_12·b_1_2
  86. b_6_60·b_5_41 + b_2_5·b_2_62·b_5_41 + b_2_52·b_2_6·b_5_40 + a_6_48·b_5_41
       + a_2_4·b_2_6·a_7_71 + a_2_4·b_2_5·b_2_63·a_1_1 + a_2_4·b_2_6·a_1_12·b_5_41
       + b_2_62·c_2_7·b_5_40 + b_2_5·c_8_124·b_1_2 + c_8_124·a_1_1·b_1_22
       + b_2_64·c_2_7·a_1_1 + b_2_6·c_2_7·a_1_12·b_5_40
  87. b_6_60·b_5_40 + b_2_63·b_5_41 + a_6_57·b_5_41 + b_2_62·a_1_12·b_5_41
       + b_2_62·a_6_48·a_1_1 + a_2_4·b_2_63·a_3_15 + a_2_4·b_2_6·a_6_57·a_1_1
       + b_2_5·c_8_124·a_1_1
  88. a_6_57·b_5_40 + b_2_64·a_3_15 + a_2_3·c_8_124·a_1_1
  89. a_6_48·b_5_41 + b_2_52·b_2_63·a_1_1 + a_2_4·b_2_62·b_5_41
       + a_2_4·b_2_5·b_2_6·b_5_40 + a_2_4·b_2_6·a_7_71 + a_2_4·b_2_5·b_2_63·a_1_1
       + a_2_42·b_2_6·b_5_40 + a_2_4·b_2_6·a_1_12·b_5_41 + a_2_42·b_2_63·a_1_1
       + c_8_124·a_1_1·b_1_22 + b_2_63·c_2_7·a_3_15 + b_2_64·c_2_7·a_1_1
       + a_2_4·c_8_124·b_1_2 + b_2_6·c_2_7·a_1_12·b_5_40 + b_2_62·c_2_7·a_1_12·a_3_15
  90. a_6_57·b_5_41 + b_2_62·a_7_71 + b_2_62·b_6_60·a_1_1 + b_2_5·b_2_64·a_1_1
       + a_6_48·a_5_37 + b_2_62·a_1_12·b_5_41 + b_2_62·a_6_48·a_1_1 + a_2_4·b_2_64·a_1_1
       + a_2_4·c_8_124·a_1_1
  91. a_6_57·a_6_48 + b_2_62·b_6_60·a_1_12 + a_2_4·b_2_62·a_1_1·b_5_40
       + a_2_4·b_2_64·a_1_12
  92. b_5_41·a_7_71 + a_6_48·b_6_60 + a_2_4·b_2_62·a_1_1·b_5_41
       + a_2_4·b_2_5·b_2_6·a_1_1·b_5_40 + a_2_42·b_2_64 + a_2_42·b_2_6·a_1_1·b_5_40
       + b_2_64·c_2_7·a_1_12 + b_2_6·c_2_7·a_6_57·a_1_12
  93. a_5_37·a_7_71 + b_2_62·a_6_48·a_1_12
  94. b_6_602 + b_2_5·b_2_62·b_6_60 + b_2_52·b_2_64 + a_6_48·b_6_60
       + a_2_4·b_2_5·b_2_64 + a_6_482 + a_2_4·b_2_62·a_1_1·b_5_41 + a_2_4·b_2_62·a_6_48
       + b_2_65·c_2_7 + b_2_52·c_8_124 + b_2_62·c_2_7·a_1_1·b_5_40 + b_2_62·c_2_7·a_6_57
       + b_2_5·c_8_124·a_1_1·b_1_2 + a_2_4·b_2_5·c_8_124 + b_2_63·c_2_7·a_1_1·a_3_15
  95. a_6_572 + b_2_64·a_1_1·a_3_15 + b_2_65·a_1_12 + b_2_62·a_6_57·a_1_12
       + a_2_3·c_8_124·a_1_12
  96. a_6_482 + a_2_4·b_2_62·a_1_1·b_5_41 + a_2_42·b_2_64 + b_2_63·c_2_7·a_1_1·a_3_15
       + a_2_4·c_8_124·a_1_1·b_1_2
  97. b_6_602 + b_2_5·b_2_62·b_6_60 + b_2_52·b_2_64 + b_2_52·b_2_6·a_1_1·b_5_40
       + a_2_4·b_2_62·b_6_60 + a_2_4·b_2_5·b_2_6·a_1_1·b_5_40 + a_2_4·b_2_6·b_6_60·a_1_12
       + a_2_42·b_2_6·a_1_1·b_5_40 + b_2_65·c_2_7 + b_2_52·c_8_124 + b_2_64·c_2_7·a_1_12
       + a_2_42·c_8_124
  98. b_5_40·a_7_71 + a_6_57·b_6_60 + b_2_63·a_1_1·b_5_41 + b_2_5·b_2_62·a_1_1·b_5_40
       + a_6_57·a_6_48 + a_2_4·b_2_62·a_1_1·b_5_40 + a_2_4·b_2_62·a_6_57
       + b_2_62·a_6_48·a_1_12 + b_2_5·c_8_124·a_1_12 + a_2_4·c_8_124·a_1_12
  99. b_5_40·a_7_71 + b_2_63·a_6_48 + a_2_4·b_2_62·a_1_1·b_5_40 + a_2_4·b_2_62·a_6_57
       + c_8_124·a_1_1·a_3_10 + b_2_5·c_8_124·a_1_12
  100. a_6_57·a_7_71 + b_2_63·a_1_12·b_5_41 + a_2_4·b_2_65·a_1_1 + b_2_62·a_1_12·a_7_71
  101. b_6_60·a_7_71 + b_2_52·b_2_64·a_1_1 + a_2_4·b_2_63·b_5_41
       + a_2_4·b_2_5·b_2_62·b_5_40 + a_6_48·a_7_71 + a_2_4·b_2_62·a_7_71
       + a_2_4·b_2_62·b_6_60·a_1_1 + b_2_64·c_2_7·a_3_15 + b_2_65·c_2_7·a_1_1
       + b_2_52·c_8_124·a_1_1 + a_2_4·b_2_6·c_8_124·b_1_2 + b_2_62·c_2_7·a_1_12·b_5_40
       + b_2_63·c_2_7·a_1_12·a_3_15 + a_2_3·c_2_7·c_8_124·a_1_1
  102. a_6_48·a_7_71 + a_2_4·b_2_62·b_6_60·a_1_1 + a_2_42·b_2_62·b_5_40
       + a_2_42·b_2_64·a_1_1 + b_2_62·c_2_7·a_6_57·a_1_1 + a_2_4·b_2_5·c_8_124·a_1_1
       + a_2_42·c_8_124·a_1_1
  103. a_7_712 + a_2_4·b_2_63·a_1_1·b_5_41 + a_2_42·b_2_65
       + a_2_4·b_2_62·b_6_60·a_1_12 + a_2_42·b_2_62·a_1_1·b_5_40
       + b_2_64·c_2_7·a_1_1·a_3_15 + a_2_4·b_2_6·c_8_124·a_1_1·b_1_2
       + b_2_62·c_2_7·a_6_57·a_1_12 + a_2_4·b_2_5·c_8_124·a_1_12
       + a_2_3·c_2_7·c_8_124·a_1_12

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 14.
  • 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_2_7, a Duflot regular element of degree 2
    2. c_8_124, a Duflot regular element of degree 8
    3. b_1_22 + b_2_6 + b_2_5, an element of degree 2
    4. b_1_22, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 6, 8, 10].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].

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. a_2_3 → 0, an element of degree 2
  5. a_2_4 → 0, an element of degree 2
  6. b_2_5 → 0, an element of degree 2
  7. b_2_6 → 0, an element of degree 2
  8. c_2_7 → c_1_02, an element of degree 2
  9. a_3_10 → 0, an element of degree 3
  10. a_3_15 → 0, an element of degree 3
  11. a_5_37 → 0, an element of degree 5
  12. b_5_40 → 0, an element of degree 5
  13. b_5_41 → 0, an element of degree 5
  14. a_6_57 → 0, an element of degree 6
  15. a_6_48 → 0, an element of degree 6
  16. b_6_60 → 0, an element of degree 6
  17. a_7_71 → 0, an element of degree 7
  18. c_8_124 → c_1_18, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 4

  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. a_2_3 → 0, an element of degree 2
  5. a_2_4 → 0, an element of degree 2
  6. b_2_5 → c_1_2·c_1_3, an element of degree 2
  7. b_2_6 → c_1_32, an element of degree 2
  8. c_2_7 → c_1_0·c_1_2 + c_1_02, an element of degree 2
  9. a_3_10 → 0, an element of degree 3
  10. a_3_15 → 0, an element of degree 3
  11. a_5_37 → 0, an element of degree 5
  12. b_5_40 → c_1_35, an element of degree 5
  13. b_5_41 → c_1_14·c_1_2 + c_1_0·c_1_34, an element of degree 5
  14. a_6_57 → 0, an element of degree 6
  15. a_6_48 → 0, an element of degree 6
  16. b_6_60 → c_1_14·c_1_2·c_1_3 + c_1_0·c_1_35, an element of degree 6
  17. a_7_71 → 0, an element of degree 7
  18. c_8_124 → c_1_38 + c_1_14·c_1_34 + c_1_18, an element of degree 8

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