Group #43:  Extraspecial Dihedral(8)*Quaternion(8)

Magma small group library number: 50

General information about the group

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

Center abelian of type: [ 2 ]

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

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

Order of the Frattini Subgroup: 2

Exponent of G: 4

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

Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 16, 16, 16, 16, 16 ]

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 32, 32, 32, 32, 32 ]

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: 10416 , 1056 , 242 , 2432 , 263 , 264

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

of order 64 and Hall-Senior numbers: 1042 , 107 , 1082 , 155 , 159 , 160 , 162 , 167 , 168 , 171 , 1722 , 174 , 177 , 178 , 1792 , 185 , 1862