Group #49:  Dihedral(32)

Magma small group library number: 18

General information about the group

PC-Group relations:
g12 = g3	g32 = g4	g42 = g5
g1-1 g2 g1 = g2 g3		g2-1 g3 g2 = g3 g4 g5
g2-1 g4 g2 = g4 g5

Center abelian of type: [ 2 ]

Orders of the terms of the Lower Central Series: [ 32, 8, 4, 2, 1 ]

Orders of the terms of the Upper Central Series: [ 1, 2, 4, 8, 32 ]

Order of the Frattini Subgroup: 8

Exponent of G: 16

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 64 and Hall-Senior numbers: 1344 , 137 , 2442 , 2652 , 266

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

of order 64 and Hall-Senior numbers: 1342 , 138 , 140 , 265 , 266 , 267