Group #12:  Dihedral(16)

Magma small group library number: 7

General information about the group

PC-Group relations:
g12 = g3	g32 = g4	g1-1 g2 g1 = g2 g3
g2-1 g3 g2 = g3 g4

Center abelian of type: [ 2 ]

Orders of the terms of the Lower Central Series: [ 16, 4, 2, 1 ]

Orders of the terms of the Upper Central Series: [ 1, 2, 4, 16 ]

Order of the Frattini Subgroup: 4

Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 4, 4 ]

Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 4, 4 ]

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

SUPERGROUPS AND SUPERQUOTIENTS

The subindices indicate multiplicities.

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

of order 32 and Hall-Senior numbers: 234 , 26 , 442 , 492 , 50

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

of order 32 and Hall-Senior numbers: 232 , 27 , 29 , 49 , 50 , 51