Group #42:  Extraspecial Dihedral(8)*Dihedral(8)

Magma small group library number: 49

General information about the group

PC-Group relations:
g42 = g5	g1-1 g3 g1 = g3 g5
g1-1 g4 g1 = g4 g5		g2-1 g4 g2 = g4 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: [ 8, 8, 8, 8, 8, 8 ]

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

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 32, 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: 10316 , 10510 , 2412 , 242 , 259 , 260 , 261 , 262

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

of order 64 and Hall-Senior numbers: 1032 , 1062 , 107 , 154 , 156 , 157 , 158 , 161 , 163 , 164 , 165 , 166 , 1692 , 1702 , 171 , 1732 , 174 , 1752 , 1762 , 177 , 178 , 1833 , 1843 , 1852 , 186