Group #5:  Quaternion(8)

Magma small group library number: 4

General information about the group

PC-Group relations:
g12 = g3	g22 = g3	g1-1 g2 g1 = g2 g3

Center abelian of type: [ 2 ]

Orders of the terms of the Lower Central Series: [ 8, 2, 1 ]

Orders of the terms of the Upper Central Series: [ 1, 2, 8 ]

Order of the Frattini Subgroup: 2

Exponent of G: 4

Orders of the Maximal Elementary Abelian Subgroups: [ 2 ]

Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 8 ]

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 8 ]

SUPERGROUPS AND SUPERQUOTIENTS

The subindices indicate multiplicities.

This group is a maximal subgroup of the non-abelian groups

of order 16 and Hall-Senior numbers: 74 , 8 , 13 , 142

This group is a maximal quotient of the non-abelian groups

of order 16 and Hall-Senior numbers: 72 , 10