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Cohomology of group number 1886 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 4 minimal generators and exponent 8.
- It is non-abelian.
- It has p-Rank 4.
- Its center has rank 2.
- It has 3 conjugacy classes of maximal elementary abelian subgroups, which are of rank 3, 3 and 4, respectively.
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
( − 1) · (t6 − t5 − t4 + t3 − 1) (t − 1)4 · (t2 + 1) · (t4 + 1) - The a-invariants are -∞,-∞,-6,-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 11 minimal generators of maximal degree 8:
-
b_1_0 , an element of degree 1 -
b_1_1 , an element of degree 1 -
b_1_2 , an element of degree 1 -
b_1_3 , an element of degree 1 -
c_2_8 , a Duflot regular element of degree 2 -
b_4_20 , an element of degree 4 -
b_5_29 , an element of degree 5 -
b_5_30 , an element of degree 5 -
b_5_31 , an element of degree 5 -
b_8_75 , an element of degree 8 -
c_8_77 , 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 29 minimal relations of maximal degree 16:
-
b_1_12 + b_1_0·b_1_1 -
b_1_22 + b_1_0·b_1_2 -
b_1_2·b_1_32 + b_1_02·b_1_1 -
b_1_02·b_1_1·b_1_32 + b_1_04·b_1_1 -
b_1_04·b_1_1 + b_4_20·b_1_2 -
b_1_04·b_1_1 + b_4_20·b_1_1 -
b_1_1·b_5_29 + b_4_20·b_1_1·b_1_3 + b_4_20·b_1_0·b_1_1 -
b_1_2·b_5_30 + b_1_2·b_5_29 + b_4_20·b_1_0·b_1_1 + c_2_8·b_1_02·b_1_2·b_1_3
+ c_2_8·b_1_03·b_1_1 -
b_1_2·b_5_29 + b_1_1·b_5_30 + b_1_0·b_5_30 + b_4_20·b_1_32 + b_4_20·b_1_1·b_1_3
+ c_2_8·b_1_02·b_1_1·b_1_3 + c_2_8·b_1_03·b_1_3 -
b_1_2·b_5_31 + b_1_0·b_5_31 + b_4_20·b_1_1·b_1_3 + b_4_20·b_1_0·b_1_3
+ c_2_8·b_1_0·b_1_33 + c_2_8·b_1_0·b_1_1·b_1_32 + c_2_8·b_1_02·b_1_32
+ c_2_8·b_1_02·b_1_1·b_1_3 -
b_1_2·b_5_31 + b_1_2·b_5_29 + b_1_1·b_5_31 + b_4_20·b_1_1·b_1_3 + b_4_20·b_1_0·b_1_1
+ c_2_8·b_1_1·b_1_33 + c_2_8·b_1_02·b_1_1·b_1_3 -
b_1_32·b_5_31 + b_1_02·b_5_31 + b_1_02·b_5_30 + b_4_20·b_1_33
+ b_4_20·b_1_0·b_1_32 + b_4_20·b_1_0·b_1_1·b_1_3 + b_4_20·b_1_02·b_1_3
+ b_4_20·b_1_02·b_1_1 + c_2_8·b_1_35 + c_2_8·b_1_1·b_1_34 + c_2_8·b_1_0·b_1_34
+ c_2_8·b_1_02·b_1_33 + c_2_8·b_1_03·b_1_32 + c_2_8·b_1_04·b_1_3 -
b_1_03·b_5_30 + b_1_03·b_5_29 + b_4_20·b_1_02·b_1_1·b_1_3 + b_4_20·b_1_03·b_1_3
+ b_4_20·b_1_03·b_1_1 + b_4_20·b_1_04 + b_4_202 + c_2_8·b_1_0·b_1_1·b_1_34
+ c_2_8·b_1_02·b_1_34 + c_2_8·b_1_04·b_1_32 + c_2_8·b_1_05·b_1_3 -
b_1_02·b_1_32·b_5_29 + b_4_20·b_5_30 + b_4_20·b_1_0·b_1_34
+ b_4_20·b_1_02·b_1_33 + b_4_20·b_1_03·b_1_32 + b_4_20·b_1_03·b_1_1·b_1_3
+ b_4_202·b_1_1 + c_2_8·b_1_1·b_1_36 + c_2_8·b_1_0·b_1_36 + c_2_8·b_1_03·b_1_34
+ c_2_8·b_4_20·b_1_02·b_1_3 -
b_1_04·b_5_31 + b_1_04·b_5_29 + b_4_20·b_5_31 + b_4_20·b_1_03·b_1_32
+ b_4_20·b_1_05 + b_4_202·b_1_3 + b_4_202·b_1_0 + c_2_8·b_1_03·b_1_34
+ c_2_8·b_1_04·b_1_33 + c_2_8·b_4_20·b_1_33 + c_2_8·b_4_20·b_1_0·b_1_32 -
b_1_03·b_1_3·b_5_31 + b_1_03·b_1_3·b_5_29 + b_1_04·b_5_31 + b_1_04·b_5_29
+ b_1_07·b_1_2·b_1_3 + b_8_75·b_1_2 + b_4_20·b_1_02·b_1_33
+ b_4_20·b_1_03·b_1_32 + b_4_20·b_1_03·b_1_1·b_1_3 + b_4_20·b_1_04·b_1_3
+ b_4_20·b_1_05 + b_4_202·b_1_3 + b_4_202·b_1_1 + b_4_202·b_1_0
+ c_2_8·b_1_1·b_1_3·b_5_30 + c_2_8·b_1_0·b_1_3·b_5_31 + c_2_8·b_1_0·b_1_3·b_5_30
+ c_2_8·b_1_0·b_1_1·b_1_35 + c_2_8·b_1_02·b_5_31 + c_2_8·b_1_02·b_1_35
+ c_2_8·b_1_04·b_1_33 + c_2_8·b_4_20·b_1_33 + c_2_8·b_4_20·b_1_0·b_1_32
+ c_2_8·b_4_20·b_1_02·b_1_3 + c_2_82·b_1_0·b_1_34 + c_2_82·b_1_0·b_1_1·b_1_33
+ c_2_83·b_1_02·b_1_1 -
b_1_0·b_1_33·b_5_30 + b_1_02·b_1_32·b_5_29 + b_1_03·b_1_3·b_5_31
+ b_1_03·b_1_3·b_5_29 + b_1_04·b_5_31 + b_1_04·b_5_29 + b_1_07·b_1_2·b_1_3
+ b_8_75·b_1_0 + b_4_20·b_5_29 + b_4_20·b_1_0·b_1_34 + b_4_20·b_1_03·b_1_1·b_1_3
+ b_4_20·b_1_05 + b_4_202·b_1_3 + b_4_202·b_1_1 + c_2_8·b_1_0·b_1_3·b_5_31
+ c_2_8·b_1_0·b_1_3·b_5_30 + c_2_8·b_1_0·b_1_36 + c_2_8·b_1_0·b_1_1·b_5_30
+ c_2_8·b_1_02·b_5_31 + c_2_8·b_1_02·b_5_30 + c_2_8·b_1_02·b_5_29
+ c_2_8·b_1_02·b_1_35 + c_2_8·b_1_03·b_1_34 + c_2_82·b_1_0·b_1_34
+ c_2_82·b_1_0·b_1_1·b_1_33 + c_2_82·b_1_03·b_1_32
+ c_2_82·b_1_03·b_1_2·b_1_3 + c_2_82·b_4_20·b_1_1 + c_2_82·b_4_20·b_1_0
+ c_2_83·b_1_0·b_1_32 -
b_1_0·b_1_33·b_5_30 + b_1_03·b_1_3·b_5_31 + b_1_03·b_1_3·b_5_29 + b_1_04·b_5_31
+ b_1_04·b_5_29 + b_8_75·b_1_1 + b_4_20·b_1_35 + b_4_20·b_1_02·b_1_33
+ b_4_20·b_1_03·b_1_32 + b_4_20·b_1_03·b_1_1·b_1_3 + b_4_20·b_1_04·b_1_3
+ b_4_20·b_1_05 + b_4_202·b_1_3 + b_4_202·b_1_0 + c_2_8·b_1_1·b_1_36
+ c_2_8·b_1_0·b_1_3·b_5_31 + c_2_8·b_1_0·b_1_3·b_5_30 + c_2_8·b_1_0·b_1_1·b_5_30
+ c_2_8·b_1_02·b_5_31 + c_2_8·b_1_02·b_5_30 + c_2_8·b_1_02·b_1_35
+ c_2_8·b_1_03·b_1_34 + c_2_8·b_1_04·b_1_33 + c_2_8·b_4_20·b_1_33
+ c_2_8·b_4_20·b_1_02·b_1_3 + c_2_8·b_4_20·b_1_02·b_1_1 + c_2_82·b_1_0·b_1_34
+ c_2_82·b_1_0·b_1_1·b_1_33 + c_2_82·b_1_04·b_1_3 + c_2_82·b_4_20·b_1_1
+ c_2_83·b_1_1·b_1_32 -
b_5_30·b_5_31 + b_5_29·b_5_31 + b_4_20·b_1_3·b_5_30 + b_4_20·b_1_3·b_5_29
+ b_4_20·b_1_0·b_5_31 + b_4_202·b_1_0·b_1_3 + c_2_8·b_1_33·b_5_30
+ c_2_8·b_1_33·b_5_29 + c_2_8·b_1_0·b_1_32·b_5_29 + c_2_8·b_1_0·b_1_1·b_1_36
+ c_2_8·b_1_02·b_1_3·b_5_31 + c_2_8·b_1_03·b_5_31 + c_2_8·b_1_03·b_5_29
+ c_2_8·b_4_20·b_1_34 + c_2_8·b_4_20·b_1_0·b_1_33 + c_2_8·b_4_20·b_1_02·b_1_32
+ c_2_8·b_4_20·b_1_02·b_1_1·b_1_3 + c_2_8·b_4_20·b_1_04 + c_2_8·b_4_202
+ c_2_82·b_1_0·b_1_1·b_1_34 + c_2_82·b_1_03·b_1_33 -
b_5_312 + b_5_30·b_5_31 + b_5_29·b_5_31 + b_1_04·b_1_3·b_5_29 + b_4_20·b_1_3·b_5_31
+ b_4_20·b_1_3·b_5_30 + b_4_20·b_1_3·b_5_29 + b_4_20·b_1_0·b_5_31
+ b_4_20·b_1_03·b_1_33 + b_4_20·b_1_04·b_1_32 + b_4_20·b_1_05·b_1_3
+ b_4_202·b_1_1·b_1_3 + b_4_202·b_1_0·b_1_1 + c_8_77·b_1_0·b_1_2
+ c_2_8·b_1_33·b_5_30 + c_2_8·b_1_33·b_5_29 + c_2_8·b_1_0·b_1_32·b_5_29
+ c_2_8·b_1_0·b_1_1·b_1_36 + c_2_8·b_1_02·b_1_3·b_5_31 + c_2_8·b_1_03·b_5_29
+ c_2_8·b_1_03·b_1_35 + c_2_8·b_1_05·b_1_33 + c_2_8·b_4_20·b_1_02·b_1_32
+ c_2_8·b_4_20·b_1_03·b_1_3 + c_2_8·b_4_20·b_1_03·b_1_1 + c_2_8·b_4_20·b_1_04
+ c_2_8·b_4_202 + c_2_82·b_1_36 + c_2_82·b_1_02·b_1_34
+ c_2_82·b_1_04·b_1_32 + c_2_82·b_1_04·b_1_2·b_1_3 + c_2_82·b_4_20·b_1_1·b_1_3
+ c_2_82·b_4_20·b_1_0·b_1_1 + c_2_83·b_1_03·b_1_1 -
b_5_312 + b_5_30·b_5_31 + b_4_20·b_1_3·b_5_30 + b_4_202·b_1_32
+ b_4_202·b_1_1·b_1_3 + b_4_202·b_1_0·b_1_1 + c_8_77·b_1_1·b_1_2
+ c_2_8·b_1_33·b_5_30 + c_2_8·b_1_0·b_1_1·b_1_36 + c_2_8·b_1_02·b_1_3·b_5_31
+ c_2_8·b_4_20·b_1_34 + c_2_8·b_4_20·b_1_02·b_1_32 + c_2_8·b_4_20·b_1_03·b_1_1
+ c_2_82·b_1_36 + c_2_82·b_1_0·b_1_1·b_1_34 + c_2_83·b_1_03·b_1_1 -
b_5_292 + b_1_04·b_1_3·b_5_29 + b_4_20·b_1_3·b_5_30 + b_4_20·b_1_03·b_1_33
+ b_4_20·b_1_04·b_1_32 + b_4_20·b_1_05·b_1_3 + b_4_202·b_1_1·b_1_3
+ b_4_202·b_1_0·b_1_1 + c_8_77·b_1_0·b_1_1 + c_8_77·b_1_02 + c_2_8·b_1_1·b_1_37
+ c_2_8·b_1_0·b_1_37 + c_2_8·b_1_0·b_1_1·b_1_3·b_5_30 + c_2_8·b_1_02·b_1_3·b_5_30
+ c_2_8·b_1_02·b_1_3·b_5_29 + c_2_8·b_1_03·b_5_29 + c_2_8·b_1_04·b_1_34
+ c_2_8·b_1_05·b_1_33 + c_2_8·b_4_20·b_1_02·b_1_1·b_1_3
+ c_2_8·b_4_20·b_1_03·b_1_3 + c_2_8·b_4_20·b_1_04 + c_2_8·b_4_202
+ c_2_82·b_1_0·b_1_1·b_1_34 + c_2_82·b_1_02·b_1_34
+ c_2_82·b_1_04·b_1_2·b_1_3 + c_2_82·b_4_20·b_1_1·b_1_3
+ c_2_82·b_4_20·b_1_0·b_1_1 + c_2_82·b_4_20·b_1_02 + c_2_83·b_1_0·b_1_1·b_1_32
+ c_2_83·b_1_02·b_1_32 -
b_5_30·b_5_31 + b_5_29·b_5_30 + b_1_35·b_5_30 + b_1_0·b_1_34·b_5_29 + b_8_75·b_1_32
+ b_4_20·b_1_3·b_5_30 + b_4_20·b_1_36 + b_4_20·b_1_0·b_5_31 + b_4_20·b_1_0·b_1_35
+ b_4_20·b_1_02·b_1_34 + b_4_20·b_1_03·b_1_33 + b_4_202·b_1_32
+ b_4_202·b_1_0·b_1_3 + b_4_202·b_1_0·b_1_1 + c_2_8·b_1_38 + c_2_8·b_1_1·b_1_37
+ c_2_8·b_1_0·b_1_32·b_5_29 + c_2_8·b_1_02·b_1_3·b_5_30
+ c_2_8·b_1_02·b_1_3·b_5_29 + c_2_8·b_1_02·b_1_36 + c_2_8·b_1_03·b_1_35
+ c_2_8·b_4_20·b_1_34 + c_2_8·b_4_20·b_1_0·b_1_33 + c_2_8·b_4_20·b_1_02·b_1_32
+ c_2_82·b_1_04·b_1_32 + c_2_82·b_4_20·b_1_32 + c_2_83·b_1_34 -
b_5_312 + b_5_30·b_5_31 + b_5_302 + b_5_29·b_5_31 + b_5_292 + b_1_0·b_1_34·b_5_29
+ b_1_04·b_1_3·b_5_29 + b_8_75·b_1_0·b_1_3 + b_8_75·b_1_0·b_1_1 + b_4_20·b_1_3·b_5_31
+ b_4_20·b_1_3·b_5_30 + b_4_20·b_1_0·b_5_31 + b_4_20·b_1_0·b_1_35
+ b_4_20·b_1_02·b_1_34 + b_4_20·b_1_03·b_1_33 + b_4_20·b_1_05·b_1_3
+ b_4_202·b_1_1·b_1_3 + b_4_202·b_1_0·b_1_1 + c_8_77·b_1_02 + c_2_8·b_1_33·b_5_30
+ c_2_8·b_1_33·b_5_29 + c_2_8·b_1_38 + c_2_8·b_1_0·b_1_32·b_5_30
+ c_2_8·b_1_0·b_1_32·b_5_29 + c_2_8·b_1_0·b_1_37 + c_2_8·b_1_0·b_1_1·b_1_3·b_5_30
+ c_2_8·b_1_02·b_1_3·b_5_31 + c_2_8·b_1_02·b_1_3·b_5_30 + c_2_8·b_1_02·b_1_36
+ c_2_8·b_1_03·b_5_29 + c_2_8·b_1_03·b_1_35 + c_2_8·b_1_05·b_1_33
+ c_2_8·b_4_20·b_1_03·b_1_3 + c_2_8·b_4_20·b_1_03·b_1_1 + c_2_8·b_4_20·b_1_04
+ c_2_8·b_4_202 + c_2_82·b_1_36 + c_2_82·b_1_02·b_1_34
+ c_2_82·b_1_04·b_1_2·b_1_3 + c_2_82·b_4_20·b_1_1·b_1_3
+ c_2_82·b_4_20·b_1_0·b_1_3 + c_2_82·b_4_20·b_1_02 + c_2_83·b_1_0·b_1_33
+ c_2_83·b_1_0·b_1_1·b_1_32 + c_2_83·b_1_02·b_1_32 -
b_4_20·b_1_33·b_5_30 + b_4_20·b_1_02·b_1_3·b_5_31 + b_4_20·b_1_02·b_1_3·b_5_29
+ b_4_20·b_1_03·b_5_31 + b_4_20·b_8_75 + b_4_202·b_1_34 + b_4_202·b_1_02·b_1_32
+ b_4_202·b_1_03·b_1_1 + b_4_202·b_1_04 + c_8_77·b_1_03·b_1_2 + c_8_77·b_1_04
+ c_2_8·b_1_0·b_1_34·b_5_29 + c_2_8·b_1_03·b_1_37 + c_2_8·b_1_05·b_1_35
+ c_2_8·b_1_06·b_1_34 + c_2_8·b_4_20·b_1_3·b_5_31 + c_2_8·b_4_20·b_1_3·b_5_30
+ c_2_8·b_4_20·b_1_36 + c_2_8·b_4_20·b_1_0·b_5_31 + c_2_8·b_4_20·b_1_0·b_5_29
+ c_2_8·b_4_20·b_1_05·b_1_3 + c_2_8·b_4_202·b_1_0·b_1_3
+ c_2_8·b_4_202·b_1_0·b_1_1 + c_2_82·b_1_0·b_1_1·b_1_36
+ c_2_82·b_1_02·b_1_36 + c_2_82·b_1_03·b_1_35 + c_2_82·b_1_04·b_1_34
+ c_2_82·b_1_05·b_1_33 + c_2_82·b_4_20·b_1_34
+ c_2_82·b_4_20·b_1_02·b_1_32 + c_2_82·b_4_20·b_1_02·b_1_1·b_1_3
+ c_2_82·b_4_20·b_1_03·b_1_3 + c_2_82·b_4_20·b_1_03·b_1_1
+ c_2_82·b_4_20·b_1_04 + c_2_82·b_4_202 + c_2_83·b_1_04·b_1_32
+ c_2_83·b_4_20·b_1_32 + c_2_83·b_4_20·b_1_0·b_1_1 -
b_1_38·b_5_30 + b_1_0·b_1_37·b_5_29 + b_8_75·b_5_31 + b_8_75·b_5_29 + b_8_75·b_1_35
+ b_4_20·b_1_34·b_5_29 + b_4_20·b_1_39 + b_4_20·b_1_0·b_1_38
+ b_4_20·b_1_02·b_1_37 + b_4_20·b_1_03·b_1_36 + b_4_20·b_8_75·b_1_3
+ b_4_202·b_5_31 + b_4_202·b_1_35 + b_4_202·b_1_0·b_1_34
+ b_4_202·b_1_02·b_1_33 + b_4_202·b_1_03·b_1_32 + b_4_202·b_1_05
+ b_4_203·b_1_1 + b_4_203·b_1_0 + c_8_77·b_1_03·b_1_32
+ c_8_77·b_1_03·b_1_1·b_1_3 + c_8_77·b_1_04·b_1_2 + c_8_77·b_1_05
+ b_4_20·c_8_77·b_1_1 + b_4_20·c_8_77·b_1_0 + c_2_8·b_1_36·b_5_29 + c_2_8·b_1_311
+ c_2_8·b_1_1·b_1_310 + c_2_8·b_1_0·b_1_1·b_1_39 + c_2_8·b_1_03·b_1_38
+ c_2_8·b_1_05·b_1_36 + c_2_8·b_1_06·b_1_35 + c_2_8·b_1_07·b_1_34
+ c_2_8·b_4_20·b_1_32·b_5_29 + c_2_8·b_4_20·b_1_0·b_1_3·b_5_31
+ c_2_8·b_4_20·b_1_0·b_1_36 + c_2_8·b_4_20·b_1_02·b_5_31
+ c_2_8·b_4_20·b_1_02·b_1_35 + c_2_8·b_4_20·b_1_03·b_1_34
+ c_2_8·b_4_20·b_1_05·b_1_32 + c_2_8·b_4_20·b_1_06·b_1_3
+ c_2_8·b_4_202·b_1_02·b_1_3 + c_2_8·b_4_202·b_1_02·b_1_1
+ c_2_8·c_8_77·b_1_1·b_1_2·b_1_3 + c_2_8·c_8_77·b_1_02·b_1_2
+ c_2_8·c_8_77·b_1_02·b_1_1 + c_2_8·c_8_77·b_1_03 + c_2_82·b_1_34·b_5_30
+ c_2_82·b_1_39 + c_2_82·b_1_0·b_1_33·b_5_29 + c_2_82·b_1_0·b_1_38
+ c_2_82·b_1_0·b_1_1·b_1_37 + c_2_82·b_1_02·b_1_32·b_5_30
+ c_2_82·b_1_03·b_1_36 + c_2_82·b_1_04·b_1_35 + c_2_82·b_1_06·b_1_33
+ c_2_82·b_4_20·b_5_29 + c_2_82·b_4_20·b_1_0·b_1_34
+ c_2_82·b_4_20·b_1_03·b_1_1·b_1_3 + c_2_82·b_4_20·b_1_05
+ c_2_82·b_4_202·b_1_0 + c_2_83·b_1_32·b_5_29 + c_2_83·b_1_37
+ c_2_83·b_1_02·b_5_31 + c_2_83·b_1_02·b_5_30 + c_2_83·b_1_03·b_1_34
+ c_2_83·b_1_05·b_1_32 + c_2_83·b_4_20·b_1_33 + c_2_83·b_4_20·b_1_0·b_1_32
+ c_2_83·b_4_20·b_1_0·b_1_1·b_1_3 + c_2_83·b_4_20·b_1_02·b_1_3
+ c_2_83·b_4_20·b_1_02·b_1_1 + c_2_83·b_4_20·b_1_03 + c_2_84·b_1_35
+ c_2_84·b_1_1·b_1_34 + c_2_84·b_1_0·b_1_34 + c_2_84·b_1_02·b_1_33
+ c_2_84·b_1_03·b_1_1·b_1_3 + c_2_84·b_1_04·b_1_3 -
b_1_38·b_5_30 + b_8_75·b_5_30 + b_8_75·b_5_29 + b_8_75·b_1_35 + b_8_75·b_1_0·b_1_34
+ b_8_75·b_1_02·b_1_33 + b_4_20·b_1_39 + b_4_20·b_1_0·b_1_38
+ b_4_20·b_1_03·b_1_36 + b_4_20·b_1_04·b_1_35 + b_4_20·b_1_05·b_1_34
+ b_4_202·b_1_02·b_1_33 + b_4_202·b_1_03·b_1_1·b_1_3 + b_4_202·b_1_05
+ b_4_203·b_1_3 + b_4_203·b_1_1 + b_4_203·b_1_0 + c_8_77·b_1_0·b_1_1·b_1_33
+ c_8_77·b_1_03·b_1_1·b_1_3 + c_8_77·b_1_04·b_1_2 + c_8_77·b_1_05
+ b_4_20·c_8_77·b_1_1 + b_4_20·c_8_77·b_1_0 + c_2_8·b_1_36·b_5_30
+ c_2_8·b_1_0·b_1_35·b_5_29 + c_2_8·b_1_04·b_1_37 + c_2_8·b_1_05·b_1_36
+ c_2_8·b_1_06·b_1_35 + c_2_8·b_1_07·b_1_34 + c_2_8·b_8_75·b_1_33
+ c_2_8·b_8_75·b_1_0·b_1_32 + c_2_8·b_4_20·b_1_0·b_1_3·b_5_29
+ c_2_8·b_4_20·b_1_0·b_1_36 + c_2_8·b_4_20·b_1_02·b_1_35
+ c_2_8·b_4_20·b_1_03·b_1_34 + c_2_8·b_4_20·b_1_06·b_1_3
+ c_2_8·b_4_202·b_1_33 + c_2_8·b_4_202·b_1_02·b_1_3
+ c_2_8·b_4_202·b_1_02·b_1_1 + c_2_8·c_8_77·b_1_1·b_1_2·b_1_3
+ c_2_8·c_8_77·b_1_0·b_1_1·b_1_3 + c_2_8·c_8_77·b_1_0·b_1_1·b_1_2
+ c_2_8·c_8_77·b_1_02·b_1_2 + c_2_8·c_8_77·b_1_02·b_1_1 + c_2_8·c_8_77·b_1_03
+ c_2_82·b_1_34·b_5_30 + c_2_82·b_1_1·b_1_38 + c_2_82·b_1_0·b_1_33·b_5_29
+ c_2_82·b_1_0·b_1_38 + c_2_82·b_1_03·b_1_3·b_5_29 + c_2_82·b_1_06·b_1_33
+ c_2_82·b_8_75·b_1_2 + c_2_82·b_8_75·b_1_0 + c_2_82·b_4_20·b_1_35
+ c_2_82·b_4_20·b_1_03·b_1_32 + c_2_82·b_4_20·b_1_03·b_1_1·b_1_3
+ c_2_82·b_4_20·b_1_04·b_1_3 + c_2_82·b_4_20·b_1_05 + c_2_82·b_4_202·b_1_1
+ c_2_83·b_1_32·b_5_30 + c_2_83·b_1_32·b_5_29 + c_2_83·b_1_37
+ c_2_83·b_1_1·b_1_3·b_5_30 + c_2_83·b_1_1·b_1_36 + c_2_83·b_1_0·b_1_36
+ c_2_83·b_1_0·b_1_1·b_5_30 + c_2_83·b_1_02·b_5_30 + c_2_83·b_1_02·b_5_29
+ c_2_83·b_1_02·b_1_35 + c_2_83·b_1_03·b_1_34 + c_2_83·b_1_04·b_1_33
+ c_2_83·b_4_20·b_1_0·b_1_32 + c_2_83·b_4_20·b_1_0·b_1_1·b_1_3
+ c_2_83·b_4_20·b_1_02·b_1_1 + c_2_83·b_4_20·b_1_03 + c_2_84·b_1_35
+ c_2_84·b_1_0·b_1_34 + c_2_84·b_1_0·b_1_1·b_1_33 + c_2_84·b_1_03·b_1_2·b_1_3
+ c_2_84·b_1_03·b_1_1·b_1_3 + c_2_84·b_4_20·b_1_0 + c_2_85·b_1_0·b_1_32
+ c_2_85·b_1_02·b_1_1 -
b_1_38·b_5_30 + b_1_0·b_1_37·b_5_29 + b_1_07·b_1_3·b_5_29 + b_8_75·b_5_29
+ b_8_75·b_1_35 + b_4_20·b_1_34·b_5_29 + b_4_20·b_1_39 + b_4_20·b_1_0·b_1_38
+ b_4_20·b_1_02·b_1_37 + b_4_20·b_1_03·b_1_36 + b_4_20·b_1_06·b_1_33
+ b_4_20·b_1_07·b_1_32 + b_4_20·b_1_08·b_1_3 + b_4_20·b_8_75·b_1_0
+ b_4_202·b_1_03·b_1_1·b_1_3 + b_4_202·b_1_04·b_1_3 + b_4_203·b_1_1
+ b_4_203·b_1_0 + c_8_77·b_1_03·b_1_32 + b_4_20·c_8_77·b_1_0 + c_2_8·b_1_36·b_5_29
+ c_2_8·b_1_311 + c_2_8·b_1_1·b_1_310 + c_2_8·b_1_03·b_1_38
+ c_2_8·b_1_04·b_1_37 + c_2_8·b_1_05·b_1_3·b_5_29 + c_2_8·b_1_05·b_1_36
+ c_2_8·b_1_06·b_1_35 + c_2_8·b_1_08·b_1_33 + c_2_8·b_8_75·b_1_33
+ c_2_8·b_8_75·b_1_02·b_1_3 + c_2_8·b_4_20·b_1_37
+ c_2_8·b_4_20·b_1_0·b_1_3·b_5_29 + c_2_8·b_4_20·b_1_02·b_5_29
+ c_2_8·b_4_20·b_1_02·b_1_35 + c_2_8·b_4_20·b_1_04·b_1_33
+ c_2_8·b_4_20·b_1_06·b_1_3 + c_2_8·b_4_202·b_1_33 + c_2_8·c_8_77·b_1_02·b_1_1
+ c_2_8·c_8_77·b_1_03 + c_2_82·b_1_34·b_5_30 + c_2_82·b_1_39
+ c_2_82·b_1_1·b_1_38 + c_2_82·b_1_0·b_1_33·b_5_29
+ c_2_82·b_1_0·b_1_1·b_1_37 + c_2_82·b_1_03·b_1_3·b_5_29
+ c_2_82·b_1_04·b_5_29 + c_2_82·b_1_04·b_1_35 + c_2_82·b_1_06·b_1_33
+ c_2_82·b_4_20·b_5_30 + c_2_82·b_4_20·b_5_29 + c_2_82·b_4_20·b_1_35
+ c_2_82·b_4_20·b_1_0·b_1_34 + c_2_82·b_4_20·b_1_03·b_1_32
+ c_2_82·b_4_20·b_1_03·b_1_1·b_1_3 + c_2_82·b_4_20·b_1_05
+ c_2_82·b_4_202·b_1_1 + c_2_82·b_4_202·b_1_0 + c_2_83·b_1_32·b_5_29
+ c_2_83·b_1_37 + c_2_83·b_1_1·b_1_36 + c_2_83·b_1_0·b_1_36
+ c_2_83·b_1_04·b_1_33 + c_2_83·b_1_05·b_1_2·b_1_3 + c_2_83·b_4_20·b_1_33
+ c_2_83·b_4_20·b_1_0·b_1_1·b_1_3 + c_2_83·b_4_20·b_1_03 + c_2_84·b_1_35
+ c_2_84·b_1_02·b_1_33 + c_2_84·b_1_03·b_1_32 + c_2_84·b_4_20·b_1_1 -
b_8_75·b_1_33·b_5_30 + b_8_752 + b_4_20·b_1_0·b_1_36·b_5_29
+ b_4_20·b_8_75·b_1_34 + b_4_202·b_1_0·b_1_37 + b_4_202·b_1_02·b_1_3·b_5_31
+ b_4_202·b_1_03·b_5_31 + b_4_202·b_1_03·b_1_35 + b_4_202·b_1_07·b_1_3
+ b_4_202·b_1_08 + b_4_202·b_8_75 + b_4_203·b_1_34 + b_4_203·b_1_0·b_1_33
+ b_4_203·b_1_02·b_1_1·b_1_3 + b_4_203·b_1_03·b_1_3 + b_4_203·b_1_03·b_1_1
+ b_4_203·b_1_04 + c_8_77·b_1_03·b_1_35 + c_8_77·b_1_05·b_1_33
+ c_8_77·b_1_07·b_1_2 + c_8_77·b_1_08 + b_4_20·c_8_77·b_1_04 + b_4_202·c_8_77
+ c_2_8·b_1_39·b_5_29 + c_2_8·b_1_0·b_1_1·b_1_312 + c_2_8·b_1_02·b_1_312
+ c_2_8·b_1_05·b_1_39 + c_2_8·b_1_06·b_1_38 + c_2_8·b_1_09·b_1_35
+ c_2_8·b_1_010·b_1_34 + c_2_8·b_8_75·b_1_3·b_5_30 + c_2_8·b_8_75·b_1_3·b_5_29
+ c_2_8·b_8_75·b_1_36 + c_2_8·b_8_75·b_1_0·b_1_35 + c_2_8·b_4_20·b_1_35·b_5_29
+ c_2_8·b_4_20·b_1_310 + c_2_8·b_4_20·b_1_0·b_1_39
+ c_2_8·b_4_20·b_1_02·b_1_38 + c_2_8·b_4_20·b_1_05·b_1_35
+ c_2_8·b_4_20·b_1_08·b_1_32 + c_2_8·b_4_20·b_1_09·b_1_3
+ c_2_8·b_4_20·b_8_75·b_1_32 + c_2_8·b_4_202·b_1_3·b_5_31
+ c_2_8·b_4_202·b_1_36 + c_2_8·b_4_202·b_1_0·b_5_31
+ c_2_8·b_4_202·b_1_0·b_1_35 + c_2_8·b_4_202·b_1_02·b_1_34
+ c_2_8·b_4_202·b_1_03·b_1_33 + c_2_8·b_4_202·b_1_04·b_1_32
+ c_2_8·b_4_202·b_1_05·b_1_3 + c_2_8·b_4_202·b_1_06 + c_2_8·b_4_203·b_1_32
+ c_2_8·b_4_203·b_1_0·b_1_1 + c_2_8·b_4_203·b_1_02
+ c_2_8·c_8_77·b_1_04·b_1_32 + c_2_8·c_8_77·b_1_05·b_1_2 + c_2_8·c_8_77·b_1_06
+ c_2_8·b_4_20·c_8_77·b_1_1·b_1_3 + c_2_8·b_4_20·c_8_77·b_1_0·b_1_3
+ c_2_8·b_4_20·c_8_77·b_1_0·b_1_1 + c_2_82·b_1_37·b_5_30
+ c_2_82·b_1_0·b_1_36·b_5_29 + c_2_82·b_1_0·b_1_1·b_1_310
+ c_2_82·b_1_06·b_1_3·b_5_29 + c_2_82·b_1_06·b_1_36 + c_2_82·b_1_09·b_1_33
+ c_2_82·b_8_75·b_1_34 + c_2_82·b_8_75·b_1_02·b_1_32
+ c_2_82·b_4_20·b_1_33·b_5_29 + c_2_82·b_4_20·b_1_38
+ c_2_82·b_4_20·b_1_0·b_1_32·b_5_29 + c_2_82·b_4_20·b_1_0·b_1_37
+ c_2_82·b_4_20·b_1_02·b_1_36 + c_2_82·b_4_20·b_1_03·b_1_35
+ c_2_82·b_4_20·b_1_04·b_1_34 + c_2_82·b_4_20·b_1_08
+ c_2_82·b_4_202·b_1_0·b_1_33 + c_2_82·b_4_202·b_1_02·b_1_32
+ c_2_82·b_4_202·b_1_03·b_1_1 + c_2_82·b_4_202·b_1_04
+ c_2_82·c_8_77·b_1_0·b_1_1·b_1_2·b_1_3 + c_2_82·c_8_77·b_1_02·b_1_2·b_1_3
+ c_2_82·c_8_77·b_1_02·b_1_1·b_1_3 + c_2_82·c_8_77·b_1_03·b_1_3
+ c_2_82·c_8_77·b_1_03·b_1_1 + c_2_82·c_8_77·b_1_04 + c_2_83·b_1_310
+ c_2_83·b_1_1·b_1_39 + c_2_83·b_1_0·b_1_34·b_5_29
+ c_2_83·b_1_0·b_1_1·b_1_38 + c_2_83·b_1_02·b_1_38 + c_2_83·b_1_05·b_5_29
+ c_2_83·b_1_05·b_1_35 + c_2_83·b_1_08·b_1_32 + c_2_83·b_4_20·b_1_3·b_5_29
+ c_2_83·b_4_20·b_1_02·b_1_34 + c_2_83·b_4_202·b_1_32
+ c_2_83·b_4_202·b_1_02 + c_2_84·b_1_33·b_5_30 + c_2_84·b_1_33·b_5_29
+ c_2_84·b_1_38 + c_2_84·b_1_1·b_1_37 + c_2_84·b_1_03·b_1_35
+ c_2_84·b_1_04·b_1_34 + c_2_84·b_1_05·b_1_33 + c_2_84·b_1_06·b_1_32
+ c_2_84·b_1_06·b_1_2·b_1_3 + c_2_84·b_4_20·b_1_0·b_1_33
+ c_2_84·b_4_20·b_1_03·b_1_3 + c_2_84·b_4_20·b_1_04 + c_2_84·b_4_202
+ c_2_85·b_1_36 + c_2_85·b_1_02·b_1_34 + c_2_85·b_1_03·b_1_33
+ c_2_85·b_1_04·b_1_32 + c_2_85·b_4_20·b_1_1·b_1_3 + c_2_85·b_4_20·b_1_0·b_1_1
+ c_2_86·b_1_34
| 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 16.
- 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:
c_2_8 , a Duflot regular element of degree 2c_8_77 , a Duflot regular element of degree 8b_1_32 + b_1_0·b_1_3 + b_1_02 , an element of degree 2b_1_32 , an element of degree 2
- The Raw Filter Degree Type of that HSOP is [-1, -1, 4, 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
-
b_1_0 →0 , an element of degree 1 -
b_1_1 →0 , an element of degree 1 -
b_1_2 →0 , an element of degree 1 -
b_1_3 →0 , an element of degree 1 -
c_2_8 →c_1_02 , an element of degree 2 -
b_4_20 →0 , an element of degree 4 -
b_5_29 →0 , an element of degree 5 -
b_5_30 →0 , an element of degree 5 -
b_5_31 →0 , an element of degree 5 -
b_8_75 →0 , an element of degree 8 -
c_8_77 →c_1_18 , an element of degree 8
Restriction map to a maximal el. ab. subgp. of rank 3
-
b_1_0 →c_1_2 , an element of degree 1 -
b_1_1 →0 , an element of degree 1 -
b_1_2 →c_1_2 , an element of degree 1 -
b_1_3 →0 , an element of degree 1 -
c_2_8 →c_1_22 + c_1_0·c_1_2 + c_1_02 , an element of degree 2 -
b_4_20 →0 , an element of degree 4 -
b_5_29 →c_1_12·c_1_23 + c_1_14·c_1_2 , an element of degree 5 -
b_5_30 →c_1_12·c_1_23 + c_1_14·c_1_2 , an element of degree 5 -
b_5_31 →c_1_12·c_1_23 + c_1_14·c_1_2 , an element of degree 5 -
b_8_75 →c_1_12·c_1_26 + c_1_14·c_1_24 + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_23
+ c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22 , an element of degree 8 -
c_8_77 →c_1_12·c_1_26 + c_1_18 + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_23
+ c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22 , an element of degree 8
Restriction map to a maximal el. ab. subgp. of rank 3
-
b_1_0 →c_1_2 , an element of degree 1 -
b_1_1 →c_1_2 , an element of degree 1 -
b_1_2 →c_1_2 , an element of degree 1 -
b_1_3 →c_1_2 , an element of degree 1 -
c_2_8 →c_1_22 + c_1_0·c_1_2 + c_1_02 , an element of degree 2 -
b_4_20 →c_1_24 , an element of degree 4 -
b_5_29 →0 , an element of degree 5 -
b_5_30 →c_1_25 , an element of degree 5 -
b_5_31 →c_1_25 + c_1_12·c_1_23 + c_1_14·c_1_2 , an element of degree 5 -
b_8_75 →c_1_0·c_1_27 + c_1_03·c_1_25 + c_1_05·c_1_23 + c_1_06·c_1_22 , an element of degree 8 -
c_8_77 →c_1_28 + c_1_14·c_1_24 + c_1_18 + c_1_0·c_1_27 + c_1_0·c_1_12·c_1_25
+ c_1_0·c_1_14·c_1_23 + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22
+ c_1_03·c_1_25 + c_1_05·c_1_23 + c_1_06·c_1_22 , an element of degree 8
Restriction map to a maximal el. ab. subgp. of rank 4
-
b_1_0 →c_1_2 , an element of degree 1 -
b_1_1 →0 , an element of degree 1 -
b_1_2 →0 , an element of degree 1 -
b_1_3 →c_1_3 , an element of degree 1 -
c_2_8 →c_1_0·c_1_2 + c_1_02 , an element of degree 2 -
b_4_20 →c_1_1·c_1_23 + c_1_12·c_1_22 + c_1_0·c_1_2·c_1_32 + c_1_0·c_1_22·c_1_3 , an element of degree 4 -
b_5_29 →c_1_1·c_1_22·c_1_32 + c_1_1·c_1_23·c_1_3 + c_1_1·c_1_24 + c_1_12·c_1_2·c_1_32
+ c_1_12·c_1_22·c_1_3 + c_1_14·c_1_2 + c_1_0·c_1_22·c_1_32 + c_1_0·c_1_23·c_1_3 , an element of degree 5 -
b_5_30 →c_1_1·c_1_22·c_1_32 + c_1_12·c_1_2·c_1_32 + c_1_0·c_1_34
+ c_1_0·c_1_2·c_1_33 + c_1_0·c_1_23·c_1_3 + c_1_02·c_1_22·c_1_3 , an element of degree 5 -
b_5_31 →c_1_1·c_1_23·c_1_3 + c_1_12·c_1_22·c_1_3 + c_1_02·c_1_33
+ c_1_02·c_1_2·c_1_32 , an element of degree 5 -
b_8_75 →c_1_1·c_1_22·c_1_35 + c_1_1·c_1_26·c_1_3 + c_1_12·c_1_2·c_1_35
+ c_1_13·c_1_25 + c_1_14·c_1_23·c_1_3 + c_1_14·c_1_24 + c_1_15·c_1_23
+ c_1_16·c_1_22 + c_1_0·c_1_37 + c_1_0·c_1_2·c_1_36 + c_1_0·c_1_23·c_1_34
+ c_1_0·c_1_25·c_1_32 + c_1_0·c_1_1·c_1_22·c_1_34
+ c_1_0·c_1_1·c_1_23·c_1_33 + c_1_0·c_1_1·c_1_26 + c_1_0·c_1_12·c_1_2·c_1_34
+ c_1_0·c_1_12·c_1_22·c_1_33 + c_1_0·c_1_12·c_1_23·c_1_32
+ c_1_0·c_1_12·c_1_24·c_1_3 + c_1_0·c_1_14·c_1_2·c_1_32
+ c_1_0·c_1_14·c_1_22·c_1_3 + c_1_0·c_1_14·c_1_23 + c_1_02·c_1_36
+ c_1_02·c_1_2·c_1_35 + c_1_02·c_1_22·c_1_34 + c_1_02·c_1_24·c_1_32
+ c_1_02·c_1_1·c_1_22·c_1_33 + c_1_02·c_1_1·c_1_23·c_1_32
+ c_1_02·c_1_12·c_1_2·c_1_33 + c_1_02·c_1_12·c_1_22·c_1_32
+ c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22 + c_1_03·c_1_35
+ c_1_03·c_1_2·c_1_34 + c_1_03·c_1_22·c_1_33 + c_1_04·c_1_23·c_1_3
+ c_1_04·c_1_1·c_1_23 + c_1_04·c_1_12·c_1_22 + c_1_05·c_1_22·c_1_3
+ c_1_06·c_1_32 , an element of degree 8 -
c_8_77 →c_1_12·c_1_22·c_1_34 + c_1_12·c_1_23·c_1_33 + c_1_12·c_1_24·c_1_32
+ c_1_12·c_1_25·c_1_3 + c_1_12·c_1_26 + c_1_14·c_1_34 + c_1_14·c_1_2·c_1_33
+ c_1_14·c_1_22·c_1_32 + c_1_14·c_1_23·c_1_3 + c_1_18 + c_1_0·c_1_37
+ c_1_0·c_1_22·c_1_35 + c_1_0·c_1_23·c_1_34 + c_1_0·c_1_1·c_1_24·c_1_32
+ c_1_0·c_1_1·c_1_25·c_1_3 + c_1_0·c_1_12·c_1_23·c_1_32
+ c_1_0·c_1_14·c_1_22·c_1_3 + c_1_02·c_1_22·c_1_34
+ c_1_02·c_1_1·c_1_23·c_1_32 + c_1_02·c_1_1·c_1_24·c_1_3
+ c_1_02·c_1_1·c_1_25 + c_1_02·c_1_12·c_1_22·c_1_32
+ c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_2·c_1_3 + c_1_03·c_1_35
+ c_1_03·c_1_2·c_1_34 + c_1_03·c_1_22·c_1_33 + c_1_03·c_1_23·c_1_32
+ c_1_03·c_1_24·c_1_3 + c_1_04·c_1_22·c_1_32 + c_1_04·c_1_1·c_1_23
+ c_1_04·c_1_12·c_1_22 + c_1_05·c_1_22·c_1_3 + c_1_06·c_1_32 , 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 | ||||||||||||||||
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