The Hall-Senior number of the group G is 2.   Its isomorphism type is Abelian(4,2)
The Magma small group library number of the group is 2


Let P denote the cohomology ring of the group G, that is, P = H*(G). Then P is a quotient of
a polynomial ring in the following variables: z , y , x
The respective degrees of these variables are: 1 , 1 , 2
The ideal of relations (that is, the ideal of the polynomial ring whose quotient is the cohomology ring of the group) is generated by the following element(s): z2


SUPERGROUPS AND SUPERQUOTIENTS. A supergroup of the group G is a group which contains a maximal subgroup isomorphic to G. A superquotient of G is a group which has a maximal quotient isomorpic to G.
The subindices indicate multiplicities. That is, a subindex indicates the number of maximal subgroups/quotients that are isomorphic to G.
This group is a maximal subgroup of the non-abelian groups
of order 16 and Hall-Senior numbers: 6 , 73 , 83 , 92 , 103 , 11
This group is a maximal quotient of the non-abelian groups
of order 16 and Hall-Senior numbers: 9 , 10 , 11
Note that we only provide information about the NONABELIAN supergroups and superquotients. If the group is abelian, as in this case, then it also has abelian supergroups and superquotients, but these are easy to compute from the Abelian type. In this example, the ABELIAN supergroups and superquotients (which must always coincide) are those of type (4,2,2), (4,4) and (8,2).


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This link takes you to a TEXT file which contains all the data about the group. This text file is readable by Magma, and it can be downloaded using your browser. This Magma file is self-contained. It contains many comments describing the data. All these comments are in the form of string variables beginning with the word "comment_". Note that if you read two of these data files with Magma, the information from the first file will be overwritten by the second one, since the names of the variables are the same. MAGMA file



This link takes you to the index of groups of the given order, namely, order 8. Back to index