Group #16

Magma small group library number: 24

General information about the group

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

Center abelian of type: [ 2, 4 ]

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: [ 16 ]

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: 208 , 273 , 32 , 53 , 542 , 60 , 77 , 792 , 802 , 97 , 102 , 1062 , 1073 , 1086 , 113 , 115 , 116 , 120 , 1262 , 130 , 1632 , 164 , 1664 , 1673 , 1682 , 170 , 172 , 1742 , 176 , 178 , 179 , 1802 , 223 , 224

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

of order 64 and Hall-Senior numbers: 204 , 28 , 29 , 306 , 33 , 83 , 892 , 902 , 91 , 92 , 933 , 98 , 102