Group #34

Magma small group library number: 34

General information about the group

PC-Group relations:
g22 = g4	g32 = g5	g1-1 g2 g1 = g2 g4
g1-1 g3 g1 = g3 g5

Center abelian of type: [ 2, 2 ]

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

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

Order of the Frattini Subgroup: 4

Exponent of G: 4

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

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

Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 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: 698 , 78 , 154 , 1583 , 165 , 1702 , 176 , 184 , 1882 , 189 , 193 , 205 , 206 , 225 , 231 , 234 , 252 , 261

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

of order 64 and Hall-Senior numbers: 694 , 82 , 85 , 144 , 148 , 188 , 189 , 192 , 198 , 225 , 226