Group #8:  Abelian(2,2) x Dihedral(8)

Magma small group library number: 46

General information about the group

PC-Group relations:
g42 = g5	g1-1 g4 g1 = g4 g5

Center abelian of type: [ 2, 2, 2 ]

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

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

Order of the Frattini Subgroup: 2

Exponent of G: 4

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

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

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 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: 1228 , 143 , 18 , 432 , 44 , 47 , 683 , 696 , 713 , 73 , 74 , 84 , 85 , 1039 , 106 , 110 , 113 , 123 , 124 , 1443 , 146 , 1544 , 157 , 1692 , 170 , 201 , 202

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

of order 64 and Hall-Senior numbers: 1214 , 152 , 16 , 18 , 43 , 44 , 45 , 46 , 683 , 693 , 70 , 712 , 72 , 73 , 74 , 77 , 78 , 110 , 111 , 112 , 1542 , 155 , 157 , 158 , 159 , 160 , 169 , 170 , 171 , 172 , 241 , 242 , 243