Group #23:  Cyclic(2) x Dihedral(16)

Magma small group library number: 39

General information about the group

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

Center abelian of type: [ 2, 2 ]

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

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

Order of the Frattini Subgroup: 4

Exponent of G: 8

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

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

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

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: 4312 , 46 , 55 , 1102 , 117 , 1342 , 135 , 138 , 1884 , 195 , 198 , 2012 , 2052 , 217 , 219 , 2252 , 228 , 2413 , 244 , 247 , 256

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

of order 64 and Hall-Senior numbers: 436 , 47 , 49 , 55 , 134 , 135 , 136 , 137 , 1882 , 190 , 193 , 195 , 201 , 205 , 207 , 213 , 244 , 245