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Cohomology of group number 634 of order 128
| About the group | Ring generators | Ring relations | Completion information | Restriction maps | Back to groups of order 128 |
General information on the group
- The group has 3 minimal generators and exponent 8.
- It is non-abelian.
- It has p-Rank 3.
- Its center has rank 1.
- It has 2 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 3.
Structure of the cohomology ring
General information
- The cohomology ring is of dimension 3 and depth 1.
- The depth coincides with the Duflot bound.
- The Poincaré series is
( − 1) · (t13 − 2·t12 + 2·t11 − t10 + 2·t9 + t8 − 2·t7 + 3·t6 − 3·t5 + 3·t4 − 2·t3 + 2·t2 + 1) (t − 1)3 · (t2 + 1) · (t4 + 1) · (t8 + 1) - The a-invariants are -∞,-9,-3,-3. They were obtained using the filter regular HSOP of the Benson test.
| About the group | Ring generators | Ring relations | Completion information | Restriction maps | Back to groups of order 128 |
Ring generators
The cohomology ring has 15 minimal generators of maximal degree 16:
-
a_1_0 , a nilpotent element of degree 1 -
a_1_1 , a nilpotent element of degree 1 -
b_1_2 , an element of degree 1 -
a_2_3 , a nilpotent element of degree 2 -
b_2_4 , an element of degree 2 -
b_2_5 , an element of degree 2 -
b_2_6 , an element of degree 2 -
b_5_19 , an element of degree 5 -
b_5_20 , an element of degree 5 -
a_9_27 , a nilpotent element of degree 9 -
b_9_43 , an element of degree 9 -
b_9_44 , an element of degree 9 -
b_10_51 , an element of degree 10 -
b_10_53 , an element of degree 10 -
c_16_113 , a Duflot regular element of degree 16
| About the group | Ring generators | Ring relations | Completion information | Restriction maps | Back to groups of order 128 |
Ring relations
There are 64 minimal relations of maximal degree 20:
-
a_1_12 + a_1_02 -
a_1_0·a_1_1 + a_1_02 -
a_1_0·b_1_2 -
a_2_3·a_1_1 + a_2_3·a_1_0 -
b_2_4·a_1_1 + a_2_3·b_1_2 + a_2_3·a_1_1 -
b_2_4·a_1_0 + a_2_3·a_1_1 -
b_2_6·b_1_2 + b_2_4·b_1_2 + b_2_6·a_1_1 + b_2_6·a_1_0 + b_2_5·a_1_1 + b_2_5·a_1_0 + a_1_03 -
b_2_5·b_1_22 + b_2_42 + a_2_3·b_1_22 + a_2_32 -
b_2_5·a_1_1·b_1_2 + a_2_3·b_2_4 + a_2_32 -
b_2_6·a_1_02 + a_2_32 + a_2_3·a_1_02 -
b_2_5·b_2_6·a_1_1 + b_2_5·b_2_6·a_1_0 + b_2_52·a_1_1 + b_2_52·a_1_0
+ a_2_3·b_2_5·b_1_2 + a_2_3·b_2_4·b_1_2 + a_2_32·a_1_0 + a_2_3·a_1_03 -
a_1_1·b_5_19 + a_2_3·b_2_5·b_2_6 + a_2_3·b_2_52 + a_2_3·b_2_4·b_2_5 + a_2_32·b_2_6
+ a_2_33 -
a_1_0·b_5_19 + a_2_3·b_2_5·b_2_6 + a_2_3·b_2_52 + a_2_3·b_2_4·b_2_5 + a_2_3·b_2_42
+ a_2_32·b_2_6 + a_2_33 -
b_1_2·b_5_20 + b_1_2·b_5_19 + b_2_4·b_1_24 + b_2_4·b_2_62 + b_2_4·b_2_52
+ b_2_42·b_2_5 + b_2_43 + a_2_3·b_1_24 + a_2_3·b_2_62 + a_2_3·b_2_52
+ a_2_3·b_2_4·b_2_5 + a_2_3·b_2_42 -
b_2_4·b_2_62 + b_2_43 + a_1_1·b_5_20 + a_1_0·b_5_20 + a_2_3·b_1_24 + a_2_3·b_2_62
+ a_2_3·b_2_4·b_2_5 + a_2_3·b_2_42 + a_2_32·b_2_5 + a_2_33 -
b_2_5·b_2_62·a_1_0 + b_2_52·b_2_6·a_1_0 + a_2_3·b_5_19 + a_2_3·b_2_4·b_2_5·b_1_2
+ a_2_3·b_2_62·a_1_0 + a_2_3·b_2_52·a_1_0 + b_2_52·a_1_03 + a_2_32·b_2_6·a_1_0 -
b_2_53·b_1_2 + b_2_4·b_5_20 + b_2_4·b_5_19 + b_2_4·b_2_52·b_1_2 + b_2_42·b_1_23
+ b_2_63·a_1_1 + b_2_63·a_1_0 + b_2_5·b_2_62·a_1_0 + b_2_52·b_2_6·a_1_0
+ b_2_53·a_1_1 + b_2_53·a_1_0 + a_2_3·b_5_20 + a_2_3·b_2_4·b_2_5·b_1_2
+ a_2_3·b_2_62·a_1_0 + a_2_3·b_2_52·a_1_0 + b_2_52·a_1_03 + a_2_32·b_2_6·a_1_0 -
a_2_32·b_2_5·b_2_6·a_1_0 + a_2_32·b_2_52·a_1_0 -
b_2_4·b_2_6·b_5_19 + b_2_42·b_5_19 + a_2_3·b_2_6·b_5_19 + a_2_3·b_2_43·b_1_2
+ a_2_32·b_5_19 + a_2_3·a_1_02·b_5_20 -
b_5_192 + b_2_52·b_2_63 + b_2_54·b_2_6 + b_2_4·b_2_54 + b_2_43·b_2_52
+ b_2_44·b_2_5 + b_2_52·a_1_1·b_5_20 + b_2_52·a_1_0·b_5_20 + a_2_3·b_2_52·b_2_62
+ a_2_3·b_2_43·b_2_5 + a_2_3·b_2_44 + b_2_54·a_1_02 + a_2_32·b_2_63
+ a_2_33·b_2_62 + a_2_33·b_2_5·b_2_6 + a_2_33·b_2_52 -
a_1_1·a_9_27 + a_2_3·b_2_6·a_1_0·b_5_20 + a_2_3·b_2_5·a_1_0·b_5_20 + a_2_32·b_2_63
+ a_2_32·b_2_5·b_2_62 + b_2_5·a_1_03·b_5_20 + a_2_3·b_2_53·a_1_02
+ a_2_32·a_1_0·b_5_20 + a_2_33·b_2_62 + a_2_33·b_2_5·b_2_6 + a_2_33·b_2_52 -
a_1_0·a_9_27 + a_2_3·b_2_6·a_1_0·b_5_20 + a_2_3·b_2_5·a_1_0·b_5_20 + a_2_32·b_2_63
+ a_2_32·b_2_5·b_2_62 + b_2_5·a_1_03·b_5_20 + a_2_3·b_2_53·a_1_02
+ a_2_32·a_1_0·b_5_20 + a_2_33·b_2_62 -
b_5_202 + b_5_192 + b_2_65 + b_2_55 + b_2_42·b_1_26 + b_2_42·b_2_53 + b_2_45
+ b_1_2·a_9_27 + a_1_1·b_9_43 + b_2_5·b_2_6·a_1_0·b_5_20 + a_2_3·b_1_28
+ a_2_3·b_2_43·b_2_5 + a_2_3·b_2_44 + b_2_54·a_1_02 + a_2_3·b_2_6·a_1_0·b_5_20
+ a_2_3·b_2_5·a_1_0·b_5_20 + a_2_32·b_2_63 + a_2_32·b_2_52·b_2_6
+ a_2_32·b_2_53 + b_2_5·a_1_03·b_5_20 + a_2_3·b_2_53·a_1_02 + a_2_33·b_2_62
+ a_2_33·b_2_52 -
b_5_202 + b_2_65 + b_2_52·b_2_63 + b_2_54·b_2_6 + b_2_55 + b_2_4·b_2_54
+ b_2_42·b_1_26 + b_2_42·b_2_53 + b_2_43·b_2_52 + b_2_44·b_2_5 + b_2_45
+ a_1_0·b_9_43 + b_2_62·a_1_1·b_5_20 + b_2_62·a_1_0·b_5_20 + b_2_5·b_2_6·a_1_0·b_5_20
+ a_2_3·b_2_52·b_2_62 + a_2_3·b_2_6·a_1_0·b_5_20 + a_2_3·b_2_5·a_1_0·b_5_20
+ a_2_32·b_2_52·b_2_6 + a_2_32·b_2_53 + b_2_5·a_1_03·b_5_20
+ a_2_3·b_2_53·a_1_02 + a_2_32·a_1_0·b_5_20 + a_2_33·b_2_62 + a_2_33·b_2_52 -
b_5_192 + b_1_2·b_9_44 + b_2_52·b_1_2·b_5_19 + b_2_52·b_2_63 + b_2_54·b_2_6
+ b_2_4·b_1_23·b_5_19 + b_2_42·b_1_26 + b_2_43·b_2_52 + a_2_3·b_1_28
+ a_2_3·b_2_52·b_2_62 + a_2_3·b_2_54 + a_2_3·b_2_43·b_2_5 + a_2_3·b_2_44
+ b_2_54·a_1_02 + a_2_32·b_2_63 + b_2_5·a_1_03·b_5_20 + a_2_3·b_2_53·a_1_02
+ a_2_32·a_1_0·b_5_20 + a_2_33·b_2_52 -
b_5_202 + b_5_192 + b_2_65 + b_2_55 + b_2_42·b_1_26 + b_2_42·b_2_53 + b_2_45
+ a_1_1·b_9_44 + b_2_62·a_1_1·b_5_20 + b_2_5·b_2_6·a_1_0·b_5_20
+ a_2_3·b_2_52·b_2_62 + a_2_3·b_2_54 + a_2_3·b_2_43·b_2_5
+ a_2_3·b_2_6·a_1_0·b_5_20 + a_2_32·b_2_63 + a_2_32·b_2_52·b_2_6
+ a_2_3·b_2_53·a_1_02 + a_2_32·a_1_0·b_5_20 + a_2_33·b_2_62
+ a_2_33·b_2_5·b_2_6 + a_2_33·b_2_52 -
b_5_202 + b_2_65 + b_2_52·b_2_63 + b_2_54·b_2_6 + b_2_55 + b_2_4·b_2_54
+ b_2_42·b_1_26 + b_2_42·b_2_53 + b_2_43·b_2_52 + b_2_44·b_2_5 + b_2_45
+ a_1_0·b_9_44 + b_2_62·a_1_1·b_5_20 + b_2_5·b_2_6·a_1_0·b_5_20 + a_2_3·b_2_54
+ b_2_54·a_1_02 + a_2_3·b_2_6·a_1_0·b_5_20 + a_2_32·b_2_52·b_2_6
+ a_2_3·b_2_53·a_1_02 + a_2_33·b_2_62 + a_2_33·b_2_5·b_2_6 + a_2_33·b_2_52 -
a_2_3·a_9_27 + a_2_3·b_2_64·a_1_0 + a_2_3·b_2_53·b_2_6·a_1_0 + a_2_32·b_2_6·b_5_20
+ a_2_32·b_2_6·b_5_19 + a_2_32·b_2_5·b_5_20 + a_2_32·b_2_5·b_5_19
+ a_2_3·b_2_5·a_1_02·b_5_20 + a_2_32·b_2_63·a_1_0 + a_2_32·b_2_53·a_1_0
+ a_2_33·b_5_20 -
b_2_4·b_9_44 + b_2_4·b_2_52·b_5_20 + b_2_42·b_1_22·b_5_19 + b_2_42·b_2_5·b_5_20
+ b_2_42·b_2_5·b_5_19 + b_2_43·b_5_20 + b_2_43·b_5_19 + b_2_43·b_1_25
+ b_2_44·b_1_23 + b_2_44·b_2_5·b_1_2 + b_2_45·b_1_2 + b_2_4·a_9_27 + a_2_3·b_9_43
+ a_2_3·b_2_62·b_5_20 + a_2_3·b_2_5·b_2_6·b_5_19 + a_2_3·b_2_52·b_5_20
+ a_2_3·b_2_52·b_5_19 + a_2_3·b_2_43·b_2_5·b_1_2 + a_2_3·b_2_44·b_1_2
+ a_2_3·b_2_64·a_1_0 + a_2_3·b_2_54·a_1_0 + a_2_32·b_2_6·b_5_20
+ a_2_32·b_2_5·b_5_20 + a_2_32·b_2_5·b_5_19 + b_2_54·a_1_03
+ a_2_32·b_2_63·a_1_0 -
b_2_6·b_9_44 + b_2_6·b_9_43 + b_2_63·b_5_20 + b_2_5·b_2_62·b_5_19
+ b_2_52·b_2_6·b_5_19 + b_2_4·b_9_43 + b_2_4·b_2_52·b_5_20 + b_2_4·b_2_52·b_5_19
+ b_2_42·b_1_22·b_5_19 + b_2_42·b_2_5·b_5_20 + b_2_43·b_5_19 + b_2_43·b_1_25
+ b_2_44·b_1_23 + b_2_44·b_2_5·b_1_2 + b_2_45·b_1_2 + b_2_5·a_9_27 + b_2_55·a_1_1
+ b_2_55·a_1_0 + a_2_3·b_9_43 + a_2_3·b_2_5·b_2_6·b_5_19 + a_1_02·b_9_43
+ a_2_3·b_2_53·b_2_6·a_1_0 + a_2_3·b_2_54·a_1_0 + a_2_32·b_2_5·b_5_20
+ a_2_32·b_2_63·a_1_0 + a_2_32·b_2_53·a_1_0 -
b_2_4·a_9_27 + a_2_3·b_9_44 + a_2_3·b_9_43 + a_2_3·b_2_62·b_5_20
+ a_2_3·b_2_5·b_2_6·b_5_19 + a_2_3·b_2_52·b_5_19 + a_2_3·b_2_43·b_2_5·b_1_2
+ a_2_3·b_2_44·b_1_2 + a_2_3·b_2_64·a_1_0 + a_2_3·b_2_54·a_1_0
+ a_2_32·b_2_6·b_5_20 -
b_1_22·b_9_43 + b_10_51·b_1_2 + b_2_4·b_9_43 + b_2_4·b_1_29 + b_2_42·b_1_22·b_5_19
+ b_2_42·b_2_5·b_5_20 + b_2_43·b_1_25 + b_2_43·b_2_52·b_1_2 + b_2_45·b_1_2
+ a_1_1·b_1_2·b_9_43 + b_2_65·a_1_1 + b_2_65·a_1_0 + b_2_55·a_1_1 + b_2_55·a_1_0
+ b_2_4·a_9_27 + a_2_3·b_9_43 + a_2_3·b_2_44·b_1_2 + a_2_3·b_2_64·a_1_0
+ a_2_3·b_2_53·b_2_6·a_1_0 + a_2_32·b_2_6·b_5_20 + a_2_32·b_2_6·b_5_19
+ a_2_32·b_2_5·b_5_19 + a_2_32·b_2_53·a_1_0 + a_2_33·b_5_20 -
a_1_1·b_1_2·b_9_43 + b_10_51·a_1_1 + b_2_54·b_2_6·a_1_0 + b_2_55·a_1_0 + b_2_4·a_9_27
+ a_2_3·b_1_29 + a_2_3·b_2_44·b_1_2 + a_1_02·b_9_43 + a_2_3·b_2_64·a_1_0
+ a_2_3·b_2_54·a_1_0 + a_2_32·b_2_6·b_5_20 + a_2_32·b_2_6·b_5_19
+ a_2_3·b_2_5·a_1_02·b_5_20 + a_2_32·b_2_63·a_1_0 + a_2_32·b_2_53·a_1_0 -
b_10_51·a_1_0 + b_2_54·b_2_6·a_1_0 + b_2_55·a_1_0 + a_1_02·b_9_43
+ a_2_3·b_2_53·b_2_6·a_1_0 + a_2_3·b_2_54·a_1_0 + a_2_32·b_2_5·b_5_20
+ a_2_32·b_2_5·b_5_19 + a_2_32·b_2_53·a_1_0 + a_2_33·b_5_20 -
b_1_22·b_9_43 + b_1_26·b_5_19 + b_10_53·b_1_2 + b_2_4·b_1_24·b_5_19 + b_2_4·b_1_29
+ b_2_4·b_2_52·b_5_20 + b_2_4·b_2_52·b_5_19 + b_2_42·b_1_27 + b_2_42·b_2_5·b_5_20
+ b_2_43·b_1_25 + b_2_43·b_2_52·b_1_2 + b_2_45·b_1_2 + b_2_4·a_9_27
+ a_2_3·b_2_52·b_5_20 + a_2_3·b_2_52·b_5_19 + a_2_3·b_2_44·b_1_2
+ a_2_3·b_2_64·a_1_0 + a_2_3·b_2_53·b_2_6·a_1_0 + a_2_32·b_2_6·b_5_20
+ a_2_32·b_2_6·b_5_19 + a_2_32·b_2_5·b_5_19 + b_2_54·a_1_03 -
a_1_1·b_1_2·b_9_43 + b_10_53·a_1_1 + b_2_55·a_1_1 + b_2_4·a_9_27 + a_2_3·b_9_43
+ a_2_3·b_1_29 + a_2_3·b_2_62·b_5_20 + a_2_3·b_2_52·b_5_20
+ a_2_3·b_2_43·b_2_5·b_1_2 + a_1_02·b_9_43 + a_2_3·b_2_53·b_2_6·a_1_0
+ a_2_3·b_2_54·a_1_0 + a_2_32·b_2_6·b_5_20 + a_2_32·b_2_6·b_5_19
+ a_2_32·b_2_5·b_5_19 + a_2_32·b_2_53·a_1_0 + a_2_33·b_5_20 -
b_10_53·a_1_0 + b_2_55·a_1_0 + b_2_4·a_9_27 + a_2_3·b_9_43 + a_2_3·b_2_62·b_5_20
+ a_2_3·b_2_52·b_5_20 + a_2_3·b_2_43·b_2_5·b_1_2 + a_1_02·b_9_43
+ a_2_3·b_2_53·b_2_6·a_1_0 + a_2_3·b_2_54·a_1_0 + a_2_32·b_2_6·b_5_20
+ a_2_32·b_2_6·b_5_19 + a_2_32·b_2_5·b_5_19 + a_2_32·b_2_63·a_1_0
+ a_2_32·b_2_53·a_1_0 -
b_2_5·b_1_2·b_9_43 + b_2_4·b_1_2·b_9_43 + b_2_4·b_10_51 + b_2_4·b_2_52·b_1_2·b_5_19
+ b_2_42·b_1_28 + b_2_42·b_2_54 + b_2_43·b_1_2·b_5_19 + b_2_43·b_2_53
+ b_2_44·b_1_24 + b_2_44·b_2_52 + a_2_3·b_2_54·b_2_6 + a_2_3·b_2_55
+ a_2_3·b_2_44·b_2_5 + a_2_3·a_1_0·b_9_43 + a_2_3·b_2_5·b_2_6·a_1_0·b_5_20
+ a_2_32·b_2_52·b_2_62 + a_2_3·b_2_54·a_1_02 + a_2_32·b_2_5·a_1_0·b_5_20
+ a_2_33·b_2_5·b_2_62 + a_2_33·b_2_52·b_2_6 + a_2_33·b_2_53 -
b_2_5·a_1_1·b_9_43 + b_2_5·a_1_0·b_9_43 + a_2_3·b_1_2·b_9_43 + a_2_3·b_10_51
+ a_2_3·b_2_54·b_2_6 + a_2_3·b_2_55 + a_2_3·b_2_45 + a_2_3·a_1_0·b_9_43
+ a_2_3·b_2_5·b_2_6·a_1_0·b_5_20 + a_2_32·b_2_52·b_2_62 + a_2_32·b_2_54
+ a_2_32·b_2_5·a_1_0·b_5_20 -
b_2_4·b_1_2·b_9_43 + b_2_4·b_1_25·b_5_19 + b_2_4·b_10_53 + b_2_4·b_2_52·b_1_2·b_5_19
+ b_2_4·b_2_55 + b_2_42·b_1_23·b_5_19 + b_2_42·b_1_28 + b_2_43·b_1_26
+ b_2_43·b_2_53 + b_2_44·b_1_24 + b_2_44·b_2_52 + b_2_45·b_2_5
+ b_2_6·a_1_0·b_9_43 + b_2_63·a_1_0·b_5_20 + b_2_5·a_1_1·b_9_43 + b_2_5·a_1_0·b_9_43
+ b_2_52·b_2_6·a_1_0·b_5_20 + a_2_3·b_2_62·a_1_0·b_5_20
+ a_2_3·b_2_5·b_2_6·a_1_0·b_5_20 + a_2_3·b_2_52·a_1_0·b_5_20 + a_2_32·b_2_64
+ a_2_32·b_2_54 + b_2_52·a_1_03·b_5_20 + a_2_3·b_2_54·a_1_02
+ a_2_32·b_2_6·a_1_0·b_5_20 + a_2_32·b_2_5·a_1_0·b_5_20 + a_2_33·b_2_63
+ a_2_33·b_2_52·b_2_6 + a_2_33·b_2_53 -
b_2_6·a_1_0·b_9_43 + b_2_63·a_1_0·b_5_20 + b_2_52·b_2_6·a_1_0·b_5_20
+ a_2_3·b_1_2·b_9_43 + a_2_3·b_10_53 + a_2_3·b_2_55 + a_2_3·b_2_45
+ a_2_3·b_2_62·a_1_0·b_5_20 + a_2_3·b_2_5·b_2_6·a_1_0·b_5_20
+ a_2_3·b_2_52·a_1_0·b_5_20 + a_2_32·b_2_64 + a_2_32·b_2_54
+ a_2_3·b_2_54·a_1_02 + a_2_32·b_2_6·a_1_0·b_5_20 + a_2_33·b_2_52·b_2_6 -
b_2_5·b_2_6·a_9_27 + b_2_52·a_9_27 + a_2_3·b_2_63·b_5_19 + a_2_3·b_2_5·b_9_44
+ a_2_3·b_2_5·b_9_43 + a_2_3·b_2_5·b_2_62·b_5_19 + a_2_3·b_2_52·b_2_6·b_5_19
+ a_2_3·b_2_53·b_5_20 + a_2_3·b_2_53·b_5_19 + a_2_3·b_2_4·b_9_43
+ a_2_3·b_2_44·b_2_5·b_1_2 + b_2_53·a_1_02·b_5_20 + a_2_3·b_2_65·a_1_0
+ a_2_3·b_2_54·b_2_6·a_1_0 + a_2_32·b_2_62·b_5_20 + a_2_32·b_2_52·b_5_20
+ a_2_3·a_1_02·b_9_43 + a_2_32·b_2_54·a_1_0 + a_2_33·b_2_5·b_5_20 -
b_5_20·b_9_44 + b_5_20·b_9_43 + b_5_19·b_9_44 + b_5_19·b_9_43 + b_2_62·b_5_19·b_5_20
+ b_2_62·b_10_51 + b_2_67 + b_2_5·b_2_6·b_5_19·b_5_20 + b_2_52·b_5_19·b_5_20
+ b_2_52·b_10_51 + b_2_52·b_2_65 + b_2_53·b_2_64 + b_2_54·b_2_63
+ b_2_55·b_2_62 + b_2_57 + b_2_4·b_10_51·b_1_22 + b_2_42·b_1_210
+ b_2_42·b_10_53 + b_2_42·b_10_51 + b_2_42·b_2_55 + b_2_43·b_1_23·b_5_19
+ b_2_43·b_2_54 + b_2_44·b_1_2·b_5_19 + b_2_46·b_1_22 + b_2_46·b_2_5
+ b_5_20·a_9_27 + b_5_19·a_9_27 + b_2_64·a_1_0·b_5_20 + b_2_52·a_1_0·b_9_43
+ b_2_53·b_2_6·a_1_0·b_5_20 + b_2_54·a_1_1·b_5_20 + a_2_3·b_10_51·b_1_22
+ a_2_3·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_66 + a_2_3·b_2_5·b_2_65
+ a_2_3·b_2_53·b_2_63 + a_2_3·b_2_54·b_2_62 + a_2_3·b_2_55·b_2_6
+ a_2_3·b_2_56 + a_2_3·b_2_46 + b_2_56·a_1_02 + a_2_3·b_2_63·a_1_0·b_5_20
+ a_2_32·b_2_65 + a_2_32·b_2_52·b_2_63 + a_2_32·b_2_54·b_2_6
+ a_2_32·b_2_55 + a_2_32·b_2_52·a_1_0·b_5_20 + a_2_33·b_2_5·b_2_63
+ a_2_33·b_2_53·b_2_6 + a_2_33·b_2_54 -
b_5_19·a_9_27 + a_2_3·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_5·b_5_19·b_5_20
+ a_2_3·b_2_5·b_2_65 + a_2_3·b_2_53·b_2_63 + a_2_3·b_2_4·b_10_53
+ a_2_3·b_2_4·b_10_51 + a_2_3·b_2_45·b_2_5 + a_2_3·b_2_46
+ a_2_3·b_2_52·b_2_6·a_1_0·b_5_20 + a_2_3·b_2_53·a_1_0·b_5_20 + a_2_32·b_2_65
+ a_2_32·b_2_5·b_2_64 + a_2_32·b_2_52·b_2_63 + a_2_32·b_2_53·b_2_62
+ a_2_32·b_2_55 + a_2_33·b_2_5·b_2_63 -
b_5_19·b_9_44 + b_2_5·b_2_6·b_10_53 + b_2_52·b_5_19·b_5_20 + b_2_52·b_10_53
+ b_2_53·b_2_64 + b_2_54·b_2_63 + b_2_55·b_2_62 + b_2_57 + b_2_4·b_2_5·b_10_51
+ b_2_4·b_2_56 + b_2_42·b_1_25·b_5_19 + b_2_42·b_2_52·b_1_2·b_5_19
+ b_2_42·b_2_55 + b_2_43·b_1_23·b_5_19 + b_2_43·b_2_5·b_1_2·b_5_19
+ b_2_45·b_2_52 + b_2_46·b_1_22 + b_5_19·a_9_27 + b_2_52·a_1_0·b_9_43
+ b_2_54·a_1_1·b_5_20 + b_2_54·a_1_0·b_5_20 + a_2_3·b_2_6·b_10_53
+ a_2_3·b_2_53·b_2_63 + a_2_3·b_2_54·b_2_62 + a_2_3·b_2_55·b_2_6
+ a_2_3·b_2_56 + a_2_3·b_2_4·b_10_51 + a_2_3·b_2_45·b_2_5 + b_2_56·a_1_02
+ a_2_3·b_2_52·b_2_6·a_1_0·b_5_20 + a_2_3·b_2_53·a_1_0·b_5_20
+ a_2_32·b_2_5·b_2_64 + a_2_32·b_2_53·b_2_62 + a_2_32·b_2_54·b_2_6
+ a_2_32·b_2_55 + b_2_53·a_1_03·b_5_20 + a_2_32·b_2_62·a_1_0·b_5_20
+ a_2_33·b_2_5·b_2_63 + a_2_33·b_2_53·b_2_6 -
b_5_19·b_9_44 + b_2_62·b_10_51 + b_2_5·b_2_6·b_10_53 + b_2_52·b_5_19·b_5_20
+ b_2_52·b_10_53 + b_2_53·b_2_64 + b_2_57 + b_2_4·b_2_5·b_10_51 + b_2_4·b_2_56
+ b_2_42·b_1_25·b_5_19 + b_2_42·b_10_51 + b_2_42·b_2_52·b_1_2·b_5_19
+ b_2_43·b_1_23·b_5_19 + b_2_43·b_2_5·b_1_2·b_5_19 + b_2_43·b_2_54
+ b_2_45·b_2_52 + b_2_46·b_1_22 + b_5_20·a_9_27 + b_2_52·a_1_0·b_9_43
+ b_2_53·b_2_6·a_1_0·b_5_20 + b_2_54·a_1_1·b_5_20 + b_2_54·a_1_0·b_5_20
+ a_2_3·b_10_51·b_1_22 + a_2_3·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_66
+ a_2_3·b_2_53·b_2_63 + a_2_3·b_2_54·b_2_62 + a_2_3·b_2_46
+ a_2_3·b_2_63·a_1_0·b_5_20 + a_2_3·b_2_5·a_1_0·b_9_43 + a_2_32·b_10_53
+ a_2_32·b_2_65 + a_2_32·b_2_5·b_2_64 + b_2_53·a_1_03·b_5_20
+ a_2_32·b_2_62·a_1_0·b_5_20 + a_2_32·b_2_52·a_1_0·b_5_20
+ a_2_33·b_2_5·b_2_63 + a_2_33·b_2_54 -
b_10_51·b_5_20 + b_10_51·b_5_19 + b_2_53·b_9_44 + b_2_53·b_9_43
+ b_2_53·b_2_62·b_5_20 + b_2_54·b_2_6·b_5_20 + b_2_55·b_5_20
+ b_2_4·b_10_51·b_1_23 + b_2_4·b_2_54·b_5_20 + b_2_4·b_2_54·b_5_19
+ b_2_42·b_2_5·b_9_43 + b_2_42·b_2_53·b_5_20 + b_2_42·b_2_53·b_5_19
+ b_2_43·b_2_52·b_5_20 + b_2_43·b_2_52·b_5_19 + b_2_44·b_2_5·b_5_20
+ b_2_45·b_5_20 + b_2_45·b_5_19 + b_2_45·b_1_25 + b_2_45·b_2_52·b_1_2
+ b_2_46·b_2_5·b_1_2 + a_1_0·b_5_20·b_9_43 + b_2_63·a_9_27 + b_2_67·a_1_0
+ b_2_57·a_1_1 + a_2_3·b_10_51·b_1_23 + a_2_3·b_2_64·b_5_20
+ a_2_3·b_2_5·b_2_6·b_9_43 + a_2_3·b_2_5·b_2_63·b_5_20 + a_2_3·b_2_52·b_9_43
+ a_2_3·b_2_53·b_2_6·b_5_20 + a_2_3·b_2_54·b_5_20 + a_2_3·b_2_54·b_5_19
+ a_2_3·b_2_4·b_2_5·b_9_43 + b_2_54·a_1_02·b_5_20 + a_2_3·b_2_66·a_1_0
+ a_2_3·b_2_55·b_2_6·a_1_0 + a_2_32·b_2_6·b_9_43 + a_2_32·b_2_63·b_5_20
+ a_2_32·b_2_5·b_2_62·b_5_19 + a_2_32·b_2_52·b_2_6·b_5_19
+ a_2_32·b_2_53·b_5_20 + a_2_32·b_2_53·b_5_19 + a_2_32·b_2_65·a_1_0
+ a_2_33·b_2_62·b_5_20 + a_2_33·b_2_5·b_2_6·b_5_20 -
b_1_2·b_5_19·b_9_43 + b_10_53·b_5_19 + b_10_51·b_5_20 + b_10_51·b_5_19
+ b_2_5·b_2_62·b_9_43 + b_2_5·b_2_64·b_5_20 + b_2_52·b_2_6·b_9_43
+ b_2_52·b_2_63·b_5_20 + b_2_53·b_9_44 + b_2_53·b_9_43 + b_2_55·b_5_20
+ b_2_55·b_5_19 + b_2_4·b_10_53·b_1_23 + b_2_4·b_2_52·b_9_43 + b_2_4·b_2_54·b_5_19
+ b_2_42·b_10_51·b_1_2 + b_2_43·b_9_43 + b_2_44·b_1_22·b_5_19
+ b_2_45·b_2_52·b_1_2 + b_2_46·b_2_5·b_1_2 + a_1_0·b_5_20·b_9_43 + b_2_63·a_9_27
+ b_2_67·a_1_0 + b_2_57·a_1_1 + a_2_3·b_2_62·b_9_43 + a_2_3·b_2_64·b_5_19
+ a_2_3·b_2_5·b_2_63·b_5_20 + a_2_3·b_2_52·b_2_62·b_5_20 + a_2_3·b_2_54·b_5_20
+ a_2_3·b_2_4·b_2_5·b_9_43 + a_2_3·b_2_42·b_9_43 + a_2_3·b_2_46·b_1_2
+ b_2_54·a_1_02·b_5_20 + a_2_3·b_2_66·a_1_0 + a_2_3·b_2_56·a_1_0
+ a_2_32·b_2_6·b_9_43 + a_2_32·b_2_52·b_2_6·b_5_19 + a_2_32·b_2_53·b_5_20
+ a_2_32·b_2_53·b_5_19 + a_2_3·b_2_5·a_1_02·b_9_43 + a_2_32·b_2_65·a_1_0
+ a_2_32·b_2_55·a_1_0 + a_2_33·b_2_5·b_2_6·b_5_20 + a_2_33·b_2_52·b_5_20 -
b_2_6·b_10_51·b_5_19 + b_2_54·b_2_62·b_5_19 + b_2_55·b_2_6·b_5_19
+ b_2_4·b_10_51·b_5_19 + b_2_4·b_2_55·b_5_19 + b_2_42·b_2_54·b_5_19
+ a_2_3·b_2_5·b_2_62·b_9_43 + a_2_3·b_2_52·b_2_6·b_9_43
+ a_2_3·b_2_52·b_2_63·b_5_20 + a_2_3·b_2_52·b_2_63·b_5_19
+ a_2_3·b_2_53·b_2_62·b_5_20 + a_2_3·b_2_42·b_2_5·b_9_43 + a_2_3·b_2_43·b_9_43
+ a_2_3·b_2_46·b_2_5·b_1_2 + a_2_3·a_1_0·b_5_20·b_9_43 + a_2_3·b_2_67·a_1_0
+ a_2_3·b_2_57·a_1_0 + a_2_32·b_2_62·b_9_43 + a_2_32·b_2_64·b_5_19
+ a_2_32·b_2_5·b_2_6·b_9_43 + a_2_32·b_2_52·b_2_62·b_5_20
+ a_2_32·b_2_52·b_2_62·b_5_19 + a_2_32·b_2_53·b_2_6·b_5_20
+ a_2_32·b_2_54·b_5_19 + a_2_3·b_2_54·a_1_02·b_5_20
+ a_2_33·b_2_5·b_2_62·b_5_20 + a_2_33·b_2_52·b_2_6·b_5_20
+ a_2_33·b_2_53·b_5_20 -
a_9_272 + a_2_32·b_2_52·b_2_65 + a_2_32·b_2_55·b_2_62
+ a_2_32·b_2_56·b_2_6 + a_2_32·b_2_57 + a_2_32·b_2_64·a_1_0·b_5_20
+ a_2_32·b_2_54·a_1_0·b_5_20 + a_2_33·b_2_66 + a_2_33·b_2_5·b_2_65
+ a_2_33·b_2_55·b_2_6 + a_2_33·b_2_56 -
b_9_442 + b_9_43·b_9_44 + b_2_62·b_5_20·b_9_43 + b_2_69
+ b_2_5·b_2_63·b_5_19·b_5_20 + b_2_52·b_5_19·b_9_43 + b_2_52·b_2_62·b_10_53
+ b_2_52·b_2_67 + b_2_53·b_2_6·b_5_19·b_5_20 + b_2_53·b_2_6·b_10_53
+ b_2_54·b_10_51 + b_2_55·b_2_64 + b_2_57·b_2_62 + b_2_58·b_2_6 + b_2_59
+ b_2_4·b_10_51·b_1_2·b_5_19 + b_2_4·b_2_53·b_10_51 + b_2_4·b_2_58
+ b_2_42·b_10_53·b_1_24 + b_2_42·b_2_52·b_5_19·b_5_20 + b_2_42·b_2_52·b_10_51
+ b_2_43·b_1_212 + b_2_43·b_10_53·b_1_22 + b_2_44·b_5_19·b_5_20
+ b_2_44·b_1_210 + b_2_44·b_2_52·b_1_2·b_5_19 + b_2_45·b_1_23·b_5_19
+ b_2_45·b_2_54 + b_2_46·b_1_2·b_5_19 + b_2_46·b_1_26 + b_2_47·b_2_52
+ b_2_48·b_1_22 + b_2_48·b_2_5 + a_9_27·b_9_44 + b_2_66·a_1_0·b_5_20
+ b_2_55·b_2_6·a_1_0·b_5_20 + b_2_56·a_1_1·b_5_20 + b_2_56·a_1_0·b_5_20
+ a_2_3·b_10_51·b_1_26 + a_2_3·b_2_6·b_5_20·b_9_43 + a_2_3·b_2_68
+ a_2_3·b_2_5·b_2_62·b_10_53 + a_2_3·b_2_5·b_2_67
+ a_2_3·b_2_52·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_53·b_10_53 + a_2_3·b_2_53·b_2_65
+ a_2_3·b_2_55·b_2_63 + a_2_3·b_2_58 + a_2_3·b_2_43·b_10_53 + a_2_3·b_2_47·b_2_5
+ a_2_3·b_2_48 + b_2_5·a_1_02·b_5_20·b_9_43 + b_2_58·a_1_02
+ a_2_3·b_2_53·a_1_0·b_9_43 + a_2_3·b_2_55·a_1_0·b_5_20 + a_2_32·b_5_20·b_9_43
+ a_2_32·b_2_62·b_5_19·b_5_20 + a_2_32·b_2_5·b_2_6·b_5_19·b_5_20
+ a_2_32·b_2_5·b_2_66 + a_2_32·b_2_52·b_5_19·b_5_20 + a_2_32·b_2_52·b_2_65
+ a_2_32·b_2_54·b_2_63 + a_2_32·b_2_56·b_2_6 + a_2_32·b_2_57
+ a_2_33·b_2_66 + a_2_33·b_2_56 -
b_9_442 + b_9_43·b_9_44 + b_2_62·b_5_20·b_9_43 + b_2_69
+ b_2_5·b_2_63·b_5_19·b_5_20 + b_2_52·b_5_19·b_9_43 + b_2_52·b_2_62·b_10_53
+ b_2_52·b_2_67 + b_2_53·b_2_6·b_5_19·b_5_20 + b_2_53·b_2_6·b_10_53
+ b_2_54·b_10_51 + b_2_55·b_2_64 + b_2_57·b_2_62 + b_2_58·b_2_6 + b_2_59
+ b_2_4·b_10_51·b_1_2·b_5_19 + b_2_4·b_2_53·b_10_51 + b_2_4·b_2_58
+ b_2_42·b_10_53·b_1_24 + b_2_42·b_2_52·b_5_19·b_5_20 + b_2_42·b_2_52·b_10_51
+ b_2_43·b_1_212 + b_2_43·b_10_53·b_1_22 + b_2_44·b_5_19·b_5_20
+ b_2_44·b_1_210 + b_2_44·b_2_52·b_1_2·b_5_19 + b_2_45·b_1_23·b_5_19
+ b_2_45·b_2_54 + b_2_46·b_1_2·b_5_19 + b_2_46·b_1_26 + b_2_47·b_2_52
+ b_2_48·b_1_22 + b_2_48·b_2_5 + b_2_66·a_1_0·b_5_20 + b_2_52·b_5_20·a_9_27
+ b_2_55·b_2_6·a_1_0·b_5_20 + b_2_56·a_1_1·b_5_20 + b_2_56·a_1_0·b_5_20
+ a_2_3·b_10_51·b_1_26 + a_2_3·b_2_63·b_10_53 + a_2_3·b_2_5·b_5_20·b_9_43
+ a_2_3·b_2_5·b_2_62·b_5_19·b_5_20 + a_2_3·b_2_52·b_2_6·b_5_19·b_5_20
+ a_2_3·b_2_52·b_2_66 + a_2_3·b_2_53·b_5_19·b_5_20 + a_2_3·b_2_53·b_10_53
+ a_2_3·b_2_54·b_2_64 + a_2_3·b_2_56·b_2_62 + a_2_3·b_2_48
+ a_2_3·b_2_53·a_1_0·b_9_43 + a_2_3·b_2_54·b_2_6·a_1_0·b_5_20
+ a_2_32·b_5_20·b_9_43 + a_2_32·b_2_62·b_5_19·b_5_20 + a_2_32·b_2_67
+ a_2_32·b_2_5·b_2_6·b_10_53 + a_2_32·b_2_52·b_5_19·b_5_20
+ a_2_32·b_2_53·b_2_64 + a_2_32·b_2_55·b_2_62 + a_2_32·b_2_56·b_2_6
+ a_2_32·b_2_57 + a_2_32·b_2_64·a_1_0·b_5_20 + a_2_32·b_2_54·a_1_0·b_5_20
+ a_2_33·b_2_5·b_2_65 + a_2_33·b_2_56 -
b_9_43·b_9_44 + b_9_432 + b_10_53·b_1_28 + b_10_51·b_1_28 + b_2_62·b_5_20·b_9_43
+ b_2_5·b_2_63·b_5_19·b_5_20 + b_2_52·b_5_19·b_9_43 + b_2_52·b_2_62·b_10_53
+ b_2_53·b_2_6·b_5_19·b_5_20 + b_2_53·b_2_6·b_10_53 + b_2_54·b_10_51
+ b_2_57·b_2_62 + b_2_59 + b_2_4·b_10_51·b_1_2·b_5_19 + b_2_4·b_10_51·b_1_26
+ b_2_4·b_2_53·b_10_51 + b_2_42·b_1_214 + b_2_42·b_10_51·b_1_24
+ b_2_42·b_2_52·b_5_19·b_5_20 + b_2_42·b_2_57 + b_2_43·b_10_51·b_1_22
+ b_2_43·b_2_5·b_5_19·b_5_20 + b_2_43·b_2_5·b_10_51 + b_2_43·b_2_56
+ b_2_44·b_5_19·b_5_20 + b_2_44·b_1_25·b_5_19 + b_2_44·b_1_210
+ b_2_44·b_2_52·b_1_2·b_5_19 + b_2_44·b_2_55 + b_2_45·b_1_23·b_5_19
+ b_2_45·b_1_28 + b_2_45·b_2_54 + b_2_46·b_1_2·b_5_19 + b_2_46·b_1_26
+ b_2_46·b_2_53 + b_2_47·b_1_24 + b_2_48·b_1_22 + b_2_48·b_2_5 + b_2_49
+ b_10_51·a_1_1·b_1_27 + b_2_66·a_1_1·b_5_20 + b_2_66·a_1_0·b_5_20
+ b_2_52·b_5_20·a_9_27 + b_2_55·b_2_6·a_1_0·b_5_20 + b_2_56·a_1_1·b_5_20
+ b_2_56·a_1_0·b_5_20 + a_2_3·b_1_216 + a_2_3·b_2_63·b_5_19·b_5_20
+ a_2_3·b_2_5·b_5_20·b_9_43 + a_2_3·b_2_5·b_2_62·b_5_19·b_5_20
+ a_2_3·b_2_52·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_53·b_5_19·b_5_20
+ a_2_3·b_2_53·b_10_53 + a_2_3·b_2_54·b_2_64 + a_2_3·b_2_55·b_2_63
+ a_2_3·b_2_56·b_2_62 + a_2_3·b_2_43·b_10_51 + a_2_3·b_2_48
+ a_2_3·b_2_65·a_1_0·b_5_20 + a_2_3·b_2_53·a_1_0·b_9_43
+ a_2_3·b_2_54·b_2_6·a_1_0·b_5_20 + a_2_32·b_5_20·b_9_43
+ a_2_32·b_2_62·b_5_19·b_5_20 + a_2_32·b_2_5·b_2_6·b_10_53
+ a_2_32·b_2_52·b_5_19·b_5_20 + a_2_32·b_2_53·b_2_64 + a_2_32·b_2_54·b_2_63
+ a_2_32·b_2_55·b_2_62 + a_2_32·b_2_54·a_1_0·b_5_20 + a_2_33·b_2_66
+ a_2_33·b_2_5·b_2_65 + a_2_33·b_2_56 + c_16_113·b_1_22 -
a_9_27·b_9_44 + a_9_27·b_9_43 + b_2_62·b_5_20·a_9_27 + a_2_3·b_10_51·b_1_26
+ a_2_3·b_2_5·b_2_62·b_5_19·b_5_20 + a_2_3·b_2_52·b_2_66
+ a_2_3·b_2_53·b_5_19·b_5_20 + a_2_3·b_2_53·b_2_65 + a_2_3·b_2_54·b_2_64
+ a_2_3·b_2_55·b_2_63 + a_2_3·b_2_43·b_10_53 + a_2_3·b_2_47·b_2_5
+ a_2_32·b_2_5·b_2_6·b_10_53 + a_2_32·b_2_5·b_2_66
+ a_2_32·b_2_52·b_5_19·b_5_20 + a_2_32·b_2_52·b_10_53 + a_2_32·b_2_53·b_2_64
+ a_2_32·b_2_56·b_2_6 + a_2_32·b_2_57 + b_2_55·a_1_03·b_5_20
+ a_2_3·b_2_57·a_1_02 + a_2_32·b_2_64·a_1_0·b_5_20 + a_2_33·b_2_66
+ a_2_33·b_2_55·b_2_6 + a_2_33·b_2_56 + c_16_113·a_1_1·b_1_2 -
b_9_442 + b_2_54·b_2_65 + b_2_55·b_2_64 + b_2_56·b_2_63 + b_2_57·b_2_62
+ b_2_58·b_2_6 + b_2_59 + b_2_4·b_2_58 + b_2_42·b_2_57 + b_2_43·b_2_56
+ b_2_44·b_1_210 + b_2_45·b_2_54 + b_2_46·b_2_53 + b_2_48·b_1_22
+ b_2_54·a_1_0·b_9_43 + b_2_55·b_2_6·a_1_0·b_5_20 + b_2_56·a_1_1·b_5_20
+ b_2_56·a_1_0·b_5_20 + a_2_3·b_2_5·b_2_62·b_5_19·b_5_20
+ a_2_3·b_2_52·b_2_6·b_5_19·b_5_20 + a_2_3·b_2_52·b_2_66 + a_2_3·b_2_53·b_2_65
+ a_2_3·b_2_55·b_2_63 + b_2_5·a_1_02·b_5_20·b_9_43 + a_2_3·b_2_53·a_1_0·b_9_43
+ a_2_3·b_2_54·b_2_6·a_1_0·b_5_20 + a_2_3·b_2_55·a_1_0·b_5_20
+ a_2_32·b_2_62·b_5_19·b_5_20 + a_2_32·b_2_62·b_10_53
+ a_2_32·b_2_5·b_2_6·b_5_19·b_5_20 + a_2_32·b_2_52·b_10_53
+ a_2_32·b_2_55·b_2_62 + a_2_32·b_2_56·b_2_6 + a_2_32·b_2_57
+ b_2_55·a_1_03·b_5_20 + a_2_3·b_2_57·a_1_02 + a_2_32·b_2_64·a_1_0·b_5_20
+ a_2_32·b_2_54·a_1_0·b_5_20 + a_2_33·b_2_66 + a_2_33·b_2_5·b_2_65
+ a_2_33·b_2_55·b_2_6 + c_16_113·a_1_02 -
b_10_53·b_9_44 + b_10_53·b_9_43 + b_10_53·b_1_29 + b_10_51·b_1_24·b_5_19
+ b_10_51·b_1_29 + b_2_62·b_10_53·b_5_20 + b_2_52·b_2_63·b_9_43
+ b_2_52·b_2_65·b_5_20 + b_2_54·b_2_6·b_9_43 + b_2_55·b_9_44 + b_2_55·b_9_43
+ b_2_55·b_2_62·b_5_20 + b_2_56·b_2_6·b_5_20 + b_2_4·b_10_53·b_1_27
+ b_2_4·b_10_51·b_1_22·b_5_19 + b_2_4·b_10_51·b_1_27 + b_2_42·b_10_53·b_1_25
+ b_2_42·b_10_51·b_1_25 + b_2_42·b_2_53·b_9_43 + b_2_42·b_2_55·b_5_19
+ b_2_43·b_1_213 + b_2_44·b_10_51·b_1_2 + b_2_44·b_2_5·b_9_43 + b_2_45·b_1_29
+ b_2_45·b_2_52·b_5_20 + b_2_45·b_2_52·b_5_19 + b_2_46·b_2_5·b_5_20
+ b_2_47·b_1_25 + b_2_49·b_1_2 + b_10_53·a_9_27 + b_10_51·a_9_27
+ b_10_51·a_1_1·b_1_28 + b_2_55·a_9_27 + a_2_3·b_1_217
+ a_2_3·b_2_6·b_10_53·b_5_20 + a_2_3·b_2_64·b_9_43 + a_2_3·b_2_66·b_5_20
+ a_2_3·b_2_5·b_2_63·b_9_43 + a_2_3·b_2_5·b_2_65·b_5_20
+ a_2_3·b_2_5·b_2_65·b_5_19 + a_2_3·b_2_52·b_2_64·b_5_19
+ a_2_3·b_2_53·b_2_6·b_9_43 + a_2_3·b_2_53·b_2_63·b_5_20
+ a_2_3·b_2_53·b_2_63·b_5_19 + a_2_3·b_2_54·b_9_43 + a_2_3·b_2_54·b_2_62·b_5_19
+ a_2_3·b_2_55·b_2_6·b_5_20 + a_2_3·b_2_55·b_2_6·b_5_19 + a_2_3·b_2_56·b_5_20
+ a_2_3·b_2_56·b_5_19 + a_2_3·b_2_43·b_2_5·b_9_43 + a_2_3·b_2_44·b_9_43
+ a_2_3·b_2_47·b_2_5·b_1_2 + a_2_3·b_2_57·b_2_6·a_1_0 + a_2_3·b_2_58·a_1_0
+ a_2_32·b_2_63·b_9_43 + a_2_32·b_2_65·b_5_20 + a_2_32·b_2_52·b_2_6·b_9_43
+ a_2_32·b_2_52·b_2_63·b_5_19 + a_2_32·b_2_53·b_2_62·b_5_19
+ a_2_32·b_2_54·b_2_6·b_5_20 + a_2_32·b_2_55·b_5_19 + a_2_32·b_2_67·a_1_0
+ a_2_32·b_2_57·a_1_0 + a_2_33·b_2_53·b_2_6·b_5_20 + c_16_113·b_1_23 -
b_10_53·a_9_27 + b_2_55·a_9_27 + a_2_3·b_2_6·b_10_53·b_5_20 + a_2_3·b_2_64·b_9_43
+ a_2_3·b_2_66·b_5_20 + a_2_3·b_2_5·b_10_53·b_5_20 + a_2_3·b_2_5·b_2_63·b_9_43
+ a_2_3·b_2_5·b_2_65·b_5_20 + a_2_3·b_2_52·b_2_64·b_5_20
+ a_2_3·b_2_53·b_2_63·b_5_20 + a_2_3·b_2_55·b_2_6·b_5_20 + a_2_3·b_2_56·b_5_20
+ a_2_3·b_2_43·b_2_5·b_9_43 + a_2_3·b_2_68·a_1_0 + a_2_3·b_2_5·a_1_0·b_5_20·b_9_43
+ a_2_3·b_2_58·a_1_0 + a_2_32·b_2_65·b_5_20 + a_2_32·b_2_52·b_2_63·b_5_19
+ a_2_32·b_2_53·b_9_43 + a_2_32·b_2_54·b_2_6·b_5_19 + a_2_32·b_2_55·b_5_20
+ a_2_32·b_2_55·b_5_19 + b_2_58·a_1_03 + a_2_32·b_2_67·a_1_0
+ a_2_32·b_2_57·a_1_0 + a_2_33·b_2_64·b_5_20 + a_2_33·b_2_53·b_2_6·b_5_20
+ a_2_33·b_2_54·b_5_20 + c_16_113·a_1_1·b_1_22 -
b_10_51·b_9_44 + b_2_52·b_10_51·b_5_19 + b_2_54·b_2_6·b_9_43
+ b_2_54·b_2_63·b_5_20 + b_2_55·b_9_43 + b_2_55·b_2_62·b_5_20
+ b_2_55·b_2_62·b_5_19 + b_2_56·b_2_6·b_5_19 + b_2_4·b_10_51·b_1_22·b_5_19
+ b_2_4·b_2_56·b_5_20 + b_2_4·b_2_56·b_5_19 + b_2_42·b_10_51·b_1_25
+ b_2_42·b_2_55·b_5_20 + b_2_42·b_2_55·b_5_19 + b_2_43·b_2_52·b_9_43
+ b_2_44·b_2_5·b_9_43 + b_2_44·b_2_53·b_5_19 + b_2_46·b_2_5·b_5_20 + b_2_47·b_5_20
+ b_2_47·b_5_19 + b_2_47·b_1_25 + b_2_47·b_2_52·b_1_2 + b_2_48·b_1_23
+ b_2_48·b_2_5·b_1_2 + a_2_3·b_10_51·b_1_27 + a_2_3·b_2_6·b_10_53·b_5_20
+ a_2_3·b_2_5·b_10_53·b_5_20 + a_2_3·b_2_5·b_2_65·b_5_19
+ a_2_3·b_2_52·b_2_64·b_5_20 + a_2_3·b_2_53·b_2_6·b_9_43
+ a_2_3·b_2_53·b_2_63·b_5_20 + a_2_3·b_2_54·b_9_43 + a_2_3·b_2_56·b_5_20
+ a_2_3·b_2_56·b_5_19 + a_2_3·b_2_43·b_2_5·b_9_43 + a_2_3·b_2_44·b_9_43
+ b_2_56·a_1_02·b_5_20 + a_2_3·b_2_68·a_1_0 + a_2_3·b_2_57·b_2_6·a_1_0
+ a_2_32·b_2_63·b_9_43 + a_2_32·b_2_5·b_2_62·b_9_43
+ a_2_32·b_2_52·b_2_63·b_5_20 + a_2_32·b_2_54·b_2_6·b_5_20
+ a_2_33·b_2_64·b_5_20 + a_2_33·b_2_53·b_2_6·b_5_20 + a_2_33·b_2_54·b_5_20
+ c_16_113·a_1_03 -
b_10_53·b_9_44 + b_10_53·b_9_43 + b_10_51·b_9_44 + b_10_51·b_9_43
+ b_10_51·b_1_24·b_5_19 + b_2_62·b_10_53·b_5_20 + b_2_52·b_10_51·b_5_19
+ b_2_52·b_2_63·b_9_43 + b_2_52·b_2_65·b_5_20 + b_2_54·b_2_6·b_9_43
+ b_2_54·b_2_63·b_5_20 + b_2_55·b_2_62·b_5_20 + b_2_55·b_2_62·b_5_19
+ b_2_56·b_2_6·b_5_20 + b_2_57·b_5_19 + b_2_4·b_2_5·b_10_51·b_5_19
+ b_2_4·b_2_56·b_5_19 + b_2_42·b_10_51·b_5_19 + b_2_42·b_10_51·b_1_25
+ b_2_42·b_2_53·b_9_43 + b_2_42·b_2_55·b_5_19 + b_2_43·b_2_52·b_9_43
+ b_2_43·b_2_54·b_5_19 + b_2_44·b_1_211 + b_2_44·b_10_51·b_1_2
+ b_2_44·b_2_5·b_9_43 + b_2_44·b_2_53·b_5_20 + b_2_45·b_2_52·b_5_20
+ b_2_45·b_2_52·b_5_19 + b_2_46·b_1_27 + b_2_46·b_2_5·b_5_20
+ b_2_46·b_2_5·b_5_19 + b_2_47·b_1_25 + b_2_48·b_1_23 + b_2_49·b_1_2
+ b_10_51·a_9_27 + b_2_65·a_9_27 + b_2_59·a_1_1 + b_2_59·a_1_0
+ a_2_3·b_2_6·b_10_53·b_5_20 + a_2_3·b_2_66·b_5_20 + a_2_3·b_2_5·b_10_53·b_5_20
+ a_2_3·b_2_5·b_2_65·b_5_20 + a_2_3·b_2_5·b_2_65·b_5_19
+ a_2_3·b_2_52·b_2_62·b_9_43 + a_2_3·b_2_53·b_2_63·b_5_20
+ a_2_3·b_2_53·b_2_63·b_5_19 + a_2_3·b_2_54·b_9_43 + a_2_3·b_2_54·b_2_62·b_5_19
+ a_2_3·b_2_55·b_2_6·b_5_19 + b_2_56·a_1_02·b_5_20 + a_2_3·b_2_68·a_1_0
+ a_2_3·b_2_5·a_1_0·b_5_20·b_9_43 + a_2_3·b_2_57·b_2_6·a_1_0
+ a_2_32·b_10_53·b_5_20 + a_2_32·b_2_65·b_5_19 + a_2_32·b_2_5·b_2_64·b_5_20
+ a_2_32·b_2_52·b_2_63·b_5_20 + a_2_32·b_2_53·b_9_43
+ a_2_32·b_2_53·b_2_62·b_5_19 + b_2_58·a_1_03 + a_2_3·b_2_55·a_1_02·b_5_20
+ a_2_33·b_2_53·b_2_6·b_5_20 + a_2_33·b_2_54·b_5_20 + b_2_4·c_16_113·b_1_2 -
b_10_53·a_9_27 + b_10_51·a_9_27 + b_2_55·a_9_27 + a_2_3·b_2_6·b_10_53·b_5_20
+ a_2_3·b_2_64·b_9_43 + a_2_3·b_2_66·b_5_20 + a_2_3·b_2_5·b_10_53·b_5_20
+ a_2_3·b_2_5·b_2_63·b_9_43 + a_2_3·b_2_5·b_2_65·b_5_20
+ a_2_3·b_2_52·b_2_64·b_5_20 + a_2_3·b_2_53·b_2_63·b_5_20
+ a_2_3·b_2_53·b_2_63·b_5_19 + a_2_3·b_2_54·b_2_62·b_5_20
+ a_2_3·b_2_54·b_2_62·b_5_19 + a_2_3·b_2_55·b_2_6·b_5_20 + a_2_3·b_2_48·b_1_2
+ b_2_56·a_1_02·b_5_20 + a_2_32·b_10_53·b_5_20 + a_2_32·b_2_63·b_9_43
+ a_2_32·b_2_65·b_5_20 + a_2_32·b_2_65·b_5_19 + a_2_32·b_2_5·b_2_62·b_9_43
+ a_2_32·b_2_5·b_2_64·b_5_20 + a_2_32·b_2_5·b_2_64·b_5_19
+ a_2_32·b_2_52·b_2_63·b_5_19 + a_2_32·b_2_54·b_2_6·b_5_20
+ a_2_32·b_2_54·b_2_6·b_5_19 + a_2_32·b_2_55·b_5_20
+ a_2_3·b_2_55·a_1_02·b_5_20 + a_2_32·b_2_67·a_1_0 + a_2_32·b_2_57·a_1_0
+ a_2_33·b_2_64·b_5_20 + a_2_33·b_2_5·b_2_63·b_5_20
+ a_2_33·b_2_53·b_2_6·b_5_20 + a_2_3·c_16_113·b_1_2 -
b_10_53·b_9_44 + b_10_51·b_9_44 + b_2_52·b_10_53·b_5_20 + b_2_52·b_10_51·b_5_19
+ b_2_52·b_2_63·b_9_43 + b_2_52·b_2_65·b_5_20 + b_2_53·b_2_64·b_5_19
+ b_2_54·b_2_63·b_5_20 + b_2_55·b_9_44 + b_2_55·b_9_43 + b_2_55·b_2_62·b_5_20
+ b_2_55·b_2_62·b_5_19 + b_2_56·b_2_6·b_5_20 + b_2_57·b_5_20 + b_2_4·b_2_54·b_9_43
+ b_2_42·b_10_53·b_5_19 + b_2_42·b_10_53·b_1_25 + b_2_42·b_10_51·b_1_25
+ b_2_42·b_2_53·b_9_43 + b_2_42·b_2_55·b_5_20 + b_2_42·b_2_55·b_5_19
+ b_2_43·b_2_54·b_5_20 + b_2_43·b_2_54·b_5_19 + b_2_44·b_10_53·b_1_2
+ b_2_44·b_10_51·b_1_2 + b_2_44·b_2_53·b_5_19 + b_2_45·b_1_24·b_5_19
+ b_2_46·b_1_22·b_5_19 + b_2_46·b_2_5·b_5_20 + b_2_52·a_1_0·b_5_20·b_9_43
+ b_2_58·b_2_6·a_1_0 + b_2_59·a_1_0 + a_2_3·b_2_64·b_9_43 + a_2_3·b_2_66·b_5_20
+ a_2_3·b_2_5·b_10_53·b_5_20 + a_2_3·b_2_52·b_2_64·b_5_19
+ a_2_3·b_2_53·b_2_63·b_5_20 + a_2_3·b_2_53·b_2_63·b_5_19
+ a_2_3·b_2_54·b_2_62·b_5_20 + a_2_3·b_2_54·b_2_62·b_5_19
+ a_2_3·b_2_55·b_2_6·b_5_20 + a_2_3·b_2_56·b_5_20 + a_2_3·b_2_56·b_5_19
+ a_2_3·b_2_47·b_2_5·b_1_2 + b_2_56·a_1_02·b_5_20 + a_2_3·b_2_58·a_1_0
+ a_2_32·b_2_53·b_2_62·b_5_19 + a_2_32·b_2_54·b_2_6·b_5_20
+ a_2_32·b_2_55·b_5_20 + a_2_32·b_2_55·b_5_19 + a_2_33·b_2_5·b_2_63·b_5_20
+ a_2_33·b_2_53·b_2_6·b_5_20 + a_2_3·c_16_113·a_1_0 -
b_10_532 + b_10_512 + b_2_54·b_2_66 + b_2_55·b_2_65 + b_2_57·b_2_63
+ b_2_42·b_10_53·b_1_26 + b_2_42·b_10_51·b_1_26 + b_2_42·b_2_53·b_10_51
+ b_2_43·b_10_51·b_1_24 + b_2_43·b_2_52·b_5_19·b_5_20 + b_2_43·b_2_52·b_10_51
+ b_2_44·b_10_53·b_1_22 + b_2_44·b_10_51·b_1_22 + b_2_44·b_2_56
+ b_2_45·b_1_210 + b_2_45·b_10_53 + b_2_45·b_10_51 + b_2_45·b_2_55
+ b_2_46·b_1_23·b_5_19 + b_2_46·b_2_54 + b_2_47·b_1_26 + b_2_48·b_1_24
+ b_2_48·b_2_52 + b_2_49·b_1_22 + a_2_3·b_2_5·b_2_63·b_5_19·b_5_20
+ a_2_3·b_2_52·b_2_62·b_5_19·b_5_20 + a_2_3·b_2_52·b_2_67
+ a_2_3·b_2_53·b_2_66 + a_2_3·b_2_56·b_2_63 + a_2_3·b_2_57·b_2_62
+ a_2_3·b_2_44·b_10_53 + a_2_3·b_2_49 + a_2_32·b_2_63·b_5_19·b_5_20
+ a_2_32·b_2_63·b_10_53 + a_2_32·b_2_68 + a_2_32·b_2_5·b_5_20·b_9_43
+ a_2_32·b_2_52·b_2_6·b_10_53 + a_2_32·b_2_53·b_5_19·b_5_20
+ a_2_32·b_2_53·b_10_53 + a_2_32·b_2_53·b_2_65 + a_2_32·b_2_54·b_2_64
+ a_2_32·b_2_55·b_2_63 + a_2_32·b_2_56·b_2_62 + a_2_32·b_2_57·b_2_6
+ a_2_32·b_2_65·a_1_0·b_5_20 + a_2_32·b_2_55·a_1_0·b_5_20 + a_2_33·b_2_67
+ a_2_33·b_2_57 + b_2_42·c_16_113 -
b_10_532 + b_10_51·b_1_25·b_5_19 + b_10_51·b_10_53 + b_2_54·b_2_6·b_10_53
+ b_2_54·b_2_66 + b_2_55·b_10_53 + b_2_55·b_10_51 + b_2_55·b_2_65
+ b_2_57·b_2_63 + b_2_58·b_2_62 + b_2_59·b_2_6 + b_2_4·b_10_53·b_1_28
+ b_2_4·b_10_51·b_1_23·b_5_19 + b_2_4·b_10_51·b_1_28 + b_2_4·b_2_52·b_5_19·b_9_43
+ b_2_4·b_2_54·b_5_19·b_5_20 + b_2_4·b_2_54·b_10_51 + b_2_4·b_2_59
+ b_2_42·b_10_51·b_1_2·b_5_19 + b_2_42·b_10_51·b_1_26 + b_2_42·b_2_58
+ b_2_43·b_5_19·b_9_43 + b_2_43·b_10_53·b_1_24 + b_2_44·b_1_212
+ b_2_44·b_2_5·b_5_19·b_5_20 + b_2_44·b_2_5·b_10_51 + b_2_45·b_1_25·b_5_19
+ b_2_45·b_10_51 + b_2_45·b_2_52·b_1_2·b_5_19 + b_2_46·b_1_28
+ b_2_46·b_2_5·b_1_2·b_5_19 + b_2_46·b_2_54 + b_2_47·b_1_26 + b_2_48·b_2_52
+ b_2_49·b_1_22 + b_2_57·a_1_1·b_5_20 + b_2_57·a_1_0·b_5_20
+ a_2_3·b_2_62·b_5_20·b_9_43 + a_2_3·b_2_69 + a_2_3·b_2_5·b_2_6·b_5_20·b_9_43
+ a_2_3·b_2_5·b_2_63·b_5_19·b_5_20 + a_2_3·b_2_5·b_2_68
+ a_2_3·b_2_52·b_5_20·b_9_43 + a_2_3·b_2_52·b_2_62·b_10_53
+ a_2_3·b_2_53·b_2_6·b_10_53 + a_2_3·b_2_53·b_2_66 + a_2_3·b_2_54·b_2_65
+ a_2_3·b_2_56·b_2_63 + a_2_3·b_2_58·b_2_6 + a_2_3·b_2_59
+ b_2_52·a_1_02·b_5_20·b_9_43 + b_2_59·a_1_02 + a_2_3·b_2_56·a_1_0·b_5_20
+ a_2_32·b_2_68 + a_2_32·b_2_5·b_5_20·b_9_43
+ a_2_32·b_2_5·b_2_62·b_5_19·b_5_20 + a_2_32·b_2_5·b_2_62·b_10_53
+ a_2_32·b_2_52·b_2_6·b_5_19·b_5_20 + a_2_32·b_2_52·b_2_66
+ a_2_32·b_2_53·b_5_19·b_5_20 + a_2_32·b_2_56·b_2_62 + a_2_32·b_2_57·b_2_6
+ a_2_3·b_2_58·a_1_02 + a_2_32·b_2_65·a_1_0·b_5_20
+ a_2_32·b_2_55·a_1_0·b_5_20 + a_2_33·b_2_5·b_2_66 + b_2_4·c_16_113·b_1_22
+ c_16_113·a_1_1·b_1_23 + a_2_3·c_16_113·b_1_22 + a_2_3·b_2_4·c_16_113
+ a_2_3·c_16_113·a_1_02 -
b_10_532 + b_10_51·b_1_2·b_9_43 + b_2_54·b_2_66 + b_2_55·b_2_65
+ b_2_57·b_2_63 + b_2_58·b_2_62 + b_2_510 + b_2_4·b_10_53·b_1_28
+ b_2_4·b_2_59 + b_2_42·b_10_51·b_1_2·b_5_19 + b_2_42·b_2_5·b_5_19·b_9_43
+ b_2_42·b_2_53·b_10_51 + b_2_42·b_2_58 + b_2_43·b_5_19·b_9_43
+ b_2_43·b_10_53·b_1_24 + b_2_43·b_10_51·b_1_24 + b_2_43·b_2_52·b_5_19·b_5_20
+ b_2_43·b_2_52·b_10_51 + b_2_43·b_2_57 + b_2_44·b_1_212
+ b_2_44·b_2_5·b_5_19·b_5_20 + b_2_44·b_2_56 + b_2_45·b_5_19·b_5_20
+ b_2_45·b_10_51 + b_2_45·b_2_52·b_1_2·b_5_19 + b_2_46·b_1_23·b_5_19
+ b_2_46·b_1_28 + b_2_47·b_1_2·b_5_19 + b_2_47·b_1_26 + b_2_48·b_2_52
+ b_2_49·b_1_22 + b_2_49·b_2_5 + b_2_57·a_1_1·b_5_20 + b_2_57·a_1_0·b_5_20
+ a_2_3·b_2_5·b_2_63·b_5_19·b_5_20 + a_2_3·b_2_52·b_2_62·b_5_19·b_5_20
+ a_2_3·b_2_52·b_2_67 + a_2_3·b_2_53·b_2_66 + a_2_3·b_2_56·b_2_63
+ a_2_3·b_2_57·b_2_62 + a_2_3·b_2_59 + a_2_3·b_2_44·b_10_53 + a_2_3·b_2_48·b_2_5
+ a_2_3·b_2_49 + b_2_59·a_1_02 + a_2_32·b_2_63·b_5_19·b_5_20
+ a_2_32·b_2_63·b_10_53 + a_2_32·b_2_5·b_5_20·b_9_43
+ a_2_32·b_2_5·b_2_62·b_5_19·b_5_20 + a_2_32·b_2_53·b_2_65
+ a_2_32·b_2_55·b_2_63 + a_2_32·b_2_56·b_2_62 + a_2_32·b_2_58
+ b_2_56·a_1_03·b_5_20 + a_2_33·b_2_56·b_2_6 + b_2_4·c_16_113·b_1_22
+ c_16_113·a_1_1·b_1_23 + a_2_32·c_16_113
| About the group | Ring generators | Ring relations | Completion information | Restriction maps | Back to groups of order 128 |
Data used for Benson′s test
- Benson′s completion test succeeded in degree 20.
- The completion test was perfect: It applied in the last degree in which a generator or relation was found.
- The following is a filter regular homogeneous system of parameters:
c_16_113 , a Duflot regular element of degree 16b_1_24 + b_2_62 + b_2_5·b_2_6 + b_2_52 + b_2_4·b_2_6 + b_2_4·b_2_5 + b_2_42 , an element of degree 4b_2_5·b_2_62 + b_2_52·b_2_6 + b_2_4·b_2_52 + b_2_42·b_1_22 , an element of degree 6
- The Raw Filter Degree Type of that HSOP is [-1, 7, 17, 23].
- The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].
- We found that there exists some filter regular HSOP formed by the first term of the above HSOP, together with 2 elements of degree 2.
| About the group | Ring generators | Ring relations | Completion information | Restriction maps | Back to groups of order 128 |
Restriction maps
Restriction map to the greatest central el. ab. subgp., which is of rank 1
-
a_1_0 →0 , an element of degree 1 -
a_1_1 →0 , an element of degree 1 -
b_1_2 →0 , an element of degree 1 -
a_2_3 →0 , an element of degree 2 -
b_2_4 →0 , an element of degree 2 -
b_2_5 →0 , an element of degree 2 -
b_2_6 →0 , an element of degree 2 -
b_5_19 →0 , an element of degree 5 -
b_5_20 →0 , an element of degree 5 -
a_9_27 →0 , an element of degree 9 -
b_9_43 →0 , an element of degree 9 -
b_9_44 →0 , an element of degree 9 -
b_10_51 →0 , an element of degree 10 -
b_10_53 →0 , an element of degree 10 -
c_16_113 →c_1_016 , an element of degree 16
Restriction map to a maximal el. ab. subgp. of rank 3
-
a_1_0 →0 , an element of degree 1 -
a_1_1 →0 , an element of degree 1 -
b_1_2 →c_1_1 , an element of degree 1 -
a_2_3 →0 , an element of degree 2 -
b_2_4 →c_1_1·c_1_2 , an element of degree 2 -
b_2_5 →c_1_22 , an element of degree 2 -
b_2_6 →c_1_1·c_1_2 , an element of degree 2 -
b_5_19 →c_1_12·c_1_23 , an element of degree 5 -
b_5_20 →c_1_25 + c_1_1·c_1_24 + c_1_12·c_1_23 + c_1_14·c_1_2 , an element of degree 5 -
a_9_27 →0 , an element of degree 9 -
b_9_43 →c_1_29 + c_1_1·c_1_28 + c_1_14·c_1_25 + c_1_15·c_1_24 + c_1_17·c_1_22
+ c_1_02·c_1_13·c_1_24 + c_1_02·c_1_15·c_1_22 + c_1_04·c_1_1·c_1_24
+ c_1_04·c_1_13·c_1_22 + c_1_04·c_1_15 + c_1_08·c_1_1 , an element of degree 9 -
b_9_44 →c_1_29 + c_1_12·c_1_27 + c_1_13·c_1_26 + c_1_15·c_1_24 + c_1_17·c_1_22 , an element of degree 9 -
b_10_51 →c_1_210 + c_1_1·c_1_29 + c_1_14·c_1_26 + c_1_15·c_1_25 + c_1_16·c_1_24
+ c_1_18·c_1_22 + c_1_19·c_1_2 + c_1_02·c_1_13·c_1_25
+ c_1_02·c_1_14·c_1_24 + c_1_02·c_1_15·c_1_23 + c_1_02·c_1_16·c_1_22
+ c_1_04·c_1_1·c_1_25 + c_1_04·c_1_12·c_1_24 + c_1_04·c_1_13·c_1_23
+ c_1_04·c_1_14·c_1_22 + c_1_04·c_1_15·c_1_2 + c_1_04·c_1_16
+ c_1_08·c_1_1·c_1_2 + c_1_08·c_1_12 , an element of degree 10 -
b_10_53 →c_1_210 + c_1_1·c_1_29 + c_1_14·c_1_26 + c_1_15·c_1_25 + c_1_19·c_1_2
+ c_1_02·c_1_14·c_1_24 + c_1_02·c_1_16·c_1_22 + c_1_04·c_1_12·c_1_24
+ c_1_04·c_1_14·c_1_22 + c_1_04·c_1_16 + c_1_08·c_1_12 , an element of degree 10 -
c_16_113 →c_1_216 + c_1_1·c_1_215 + c_1_13·c_1_213 + c_1_18·c_1_28 + c_1_110·c_1_26
+ c_1_111·c_1_25 + c_1_114·c_1_22 + c_1_02·c_1_13·c_1_211
+ c_1_02·c_1_16·c_1_28 + c_1_02·c_1_19·c_1_25 + c_1_02·c_1_110·c_1_24
+ c_1_04·c_1_1·c_1_211 + c_1_04·c_1_15·c_1_27 + c_1_04·c_1_18·c_1_24
+ c_1_04·c_1_19·c_1_23 + c_1_04·c_1_110·c_1_22 + c_1_08·c_1_28
+ c_1_08·c_1_1·c_1_27 + c_1_08·c_1_13·c_1_25 + c_1_08·c_1_15·c_1_23
+ c_1_08·c_1_16·c_1_22 + c_1_08·c_1_18 + c_1_016 , an element of degree 16
Restriction map to a maximal el. ab. subgp. of rank 3
-
a_1_0 →0 , an element of degree 1 -
a_1_1 →0 , an element of degree 1 -
b_1_2 →0 , an element of degree 1 -
a_2_3 →0 , an element of degree 2 -
b_2_4 →0 , an element of degree 2 -
b_2_5 →c_1_22 + c_1_12 , an element of degree 2 -
b_2_6 →c_1_12 , an element of degree 2 -
b_5_19 →c_1_1·c_1_24 + c_1_13·c_1_22 , an element of degree 5 -
b_5_20 →c_1_25 + c_1_13·c_1_22 + c_1_14·c_1_2 , an element of degree 5 -
a_9_27 →0 , an element of degree 9 -
b_9_43 →c_1_29 + c_1_1·c_1_28 + c_1_12·c_1_27 + c_1_14·c_1_25 + c_1_15·c_1_24
+ c_1_16·c_1_23 + c_1_17·c_1_22 , an element of degree 9 -
b_9_44 →c_1_29 + c_1_12·c_1_27 + c_1_16·c_1_23 + c_1_18·c_1_2 , an element of degree 9 -
b_10_51 →c_1_210 + c_1_18·c_1_22 , an element of degree 10 -
b_10_53 →c_1_210 + c_1_13·c_1_27 + c_1_14·c_1_26 + c_1_16·c_1_24 + c_1_17·c_1_23
+ c_1_110 , an element of degree 10 -
c_16_113 →c_1_216 + c_1_13·c_1_213 + c_1_16·c_1_210 + c_1_17·c_1_29 + c_1_18·c_1_28
+ c_1_110·c_1_26 + c_1_114·c_1_22 + c_1_04·c_1_14·c_1_28
+ c_1_04·c_1_18·c_1_24 + c_1_08·c_1_28 + c_1_08·c_1_14·c_1_24
+ c_1_08·c_1_18 + c_1_016 , an element of degree 16
| 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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