General information, Order(G) = 64, Hall-Senior number = 46

Group #46: Cyclic(2) x Group(32)#26

Magma small group library number: 253

General information about the group

PC-Group relations:
g₁² = g₆	g₂² = g₆	g₃² = g₅ g₆	g₅² = g₆
g₁^-1 g₃ g₁ = g₃ g₅		g₁^-1 g₅ g₁ = g₅ g₆

Center abelian of type: [ 2, 4 ]
Orders of the terms of the Lower Central Series: [ 64, 4, 2, 1 ]
Orders of the terms of the Upper Central Series: [ 1, 8, 16, 64 ]
Order of the Frattini Subgroup: 4
Exponent of G: 8

Orders of the Maximal Elementary Abelian Subgroups: [ 8, 8, 8 ]
Orders of the Centralizers of the Maximal Elementary Abelian Subgroups: [ 32, 16, 16 ]
Orders of the Normalizers of the Maximal Elementary Abelian Subgroups: [ 64, 32, 32 ]