General information, Order(G) = 32, Hall-Senior number = 27

Group #27

Magma small group library number: 9

General information about the group

PC-Group relations:
g₁² = g₃	g₄² = g₅	g₁^-1 g₂ g₁ = g₂ g₄ g₅
g₁^-1 g₄ g₁ = g₄ g₅		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: 8
Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 8 ]
Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 8 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 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: 47₄ , 53₂ , 55₂ , 56 , 113₄ , 114₂ , 117₂ , 118 , 193₄ , 195₂ , 196 , 200₂ , 201₂ , 202₂ , 205₂ , 206₂ , 207₂ , 209₂ , 213₂ , 214₂ , 217 , 218 , 219 , 220 , 221₂ , 223₂ , 228₂ , 229 , 231₄ , 232₂
This group is a maximal quotient of the non-abelian groups
of order 64 and Hall-Senior numbers: 47₄ , 59₂ , 62 , 138 , 139 , 142 , 234₂ , 235 , 237 , 247 , 248 , 249