General information, Order(G) = 32, Hall-Senior number = 38

Group #38

Magma small group library number: 30

General information about the group

PC-Group relations:
g₁² = g₅	g₁^-1 g₃ g₁ = g₃ g₄
g₂^-1 g₃ g₂ = 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 ]
Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 16, 8 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 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: 73₈ , 77₂ , 80₂ , 157₂ , 160₄ , 163₃ , 164₂ , 165₄ , 167₂ , 169₄ , 172₄ , 175₂ , 176₄ , 177₄ , 178₂ , 184₃ , 185₄ , 186₂ , 251 , 260₃
This group is a maximal quotient of the non-abelian groups
of order 64 and Hall-Senior numbers: 73₄ , 84 , 86 , 89₄ , 91 , 92 , 146₂ , 148₃ , 149 , 151₃ , 152 , 213 , 214 , 215 , 216 , 223 , 224