The Hall-Senior number is 11. This group has no common name.
The Magma small group library number is 6


This page appears on the right frame by default. Here you can find information about the group itself, such as PC-relations, center type, centralizers and normalizers of maximal elementary abelian subgroups, supergroups and superquotients.



General information about the group


Since the group has order 16, it needs 4 PC-Group generators. They satisfy the following relations:
g12 = g2 g22 = g4 g1-1 g3 g1 = g3 g4


The center of the group is the abelian group of type [ 4 ]
The orders of the terms of the Lower Central Series are [ 16, 2, 1 ]
The orders of the terms of the Upper Central Series are [ 1, 4, 16 ]
The order of the Frattini Subgroup of the group G is 4
The exponent of the group G is 8


The orders of the Maximal Elementary Abelian Subgroups of G are [ 4 ]
The orders of the Centralizers of the Maximal Elementary Abelian Subgroups are [ 8 ]
The orders of the Normalizers of the Maximal Elementary Abelian Subgroups are [ 16 ]


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 32 and Hall-Senior numbers: 134 , 173 , 31 , 322 , 44 , 45 , 472 , 482
This group is a maximal quotient of the non-abelian groups
of order 32 and Hall-Senior numbers: 132 , 192 , 20 , 21