Group #12:  Cyclic(2) x Group(16)#10

Magma small group library number: 23

General information about the group

PC-Group relations:
g12 = g3	g22 = g3	g1-1 g2 g1 = g2 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: 4

Exponent of G: 4

Orders of the Maximal Elementary Abelian Subgroups: [ 8 ]

Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 32 ]

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 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: 1612 , 18 , 193 , 202 , 292 , 47 , 48 , 492 , 502 , 592 , 704 , 71 , 723 , 732 , 756 , 763 , 826 , 832 , 85 , 862 , 87 , 884 , 902 , 91 , 922 , 1073 , 114 , 116 , 129 , 132 , 1453 , 146 , 1483 , 1494 , 1503 , 151 , 1522 , 1602 , 1612 , 164 , 167 , 171 , 174 , 177 , 213 , 214 , 215 , 216

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

of order 64 and Hall-Senior numbers: 1612 , 223 , 25 , 29 , 49 , 50 , 52 , 54 , 823 , 83 , 86 , 88 , 90 , 95 , 97 , 116 , 121